Introduction to Co-ordinate Geometry
Mapping the plane
Distance between two points
Distance formula
Properties of distance
Midpoint of a line segment
Midpoint formula
This document provides an introduction to coordinate geometry and the Cartesian coordinate system. It defines key terms like coordinates, quadrants, and plotting points. The Cartesian plane is formed by the intersection of the x and y axes, with the origin at (0,0). Any point can be uniquely identified using an ordered pair (x,y) representing the distances from the x and y axes. Examples are given of plotting points and calculating distances between points on the plane using their coordinates. In summary, the document outlines the basic concepts of the Cartesian coordinate system used in coordinate geometry.
History,applications,algebra and mathematical form of plane in mathematics (p...guesta62dea
The document provides information about planes and equations of planes. It defines a plane as a flat surface that extends indefinitely in width and height but has no thickness. Various plane shapes and their area formulas are described. Different forms of equations for a straight line including slope-intercept, point-slope, two-point, and standard forms are derived from the general linear equation. Two and three-dimensional Cartesian coordinate systems are also explained.
The rectangular coordinate system (also known as Cartesian plane) was developed by René Descartes and uses two perpendicular number lines (x-axis and y-axis) that intersect at the origin (0,0) to locate points in a plane. Any point is identified with an ordered pair (x,y) denoting its distances from the x-axis and y-axis. The axes divide the plane into four quadrants, and points can be plotted or identified from their coordinates.
The rectangular coordinate system (also known as the Cartesian plane) was developed by René Descartes and uses two perpendicular number lines (the x-axis and y-axis) that intersect at the origin (0,0) to locate points in a plane. Any point is identified with an ordered pair (x,y) denoting its distances from the x-axis and y-axis. The axes divide the plane into four quadrants, and points can be plotted or identified based on their coordinates.
Coordinate geometry represents points on a number line with real numbers. The number line places positive numbers to the right of zero and negative numbers to the left.
The Cartesian coordinate system uniquely determines points in two or three dimensional space using perpendicular x and y axes intersecting at the origin. René Descartes developed this system, linking algebra and geometry by describing curves and lines with equations.
The coordinate plane has perpendicular x and y axes. Points are located using their x and y coordinates, which represent horizontal and vertical distances from the origin. The plane is divided into four quadrants numbered counter-clockwise from the top right. Ordered pairs notation (x,y) specifies a point's location by listing the x coordinate first.
The document discusses key concepts about linear equations in two variables including:
1) It describes the Cartesian coordinate plane and how to plot points based on their x and y coordinates.
2) It explains how to find the slope, y-intercept, and x-intercept of a linear equation graphically and algebraically.
3) It provides examples of rewriting linear equations in slope-intercept form (y=mx+b) and using intercepts and slopes to graph lines on the coordinate plane.
Beginning direct3d gameprogrammingmath01_primer_20160324_jintaeksJinTaek Seo
This document provides an introduction to mathematics concepts for direct3D game programming, including:
- 2D rotation formulas for rotating a point about an angle
- Definitions of domain, codomain, exponentiation, factorial, square root, and cubic root
- Explanations of inverse functions, Pythagorean theorem, summation notation, and practice problems for various concepts
- Overviews of the Cartesian coordinate system, trigonometric functions, and how to implement them in programs
The document discusses coordinate geometry and the Cartesian coordinate system. It describes how René Descartes proposed using an ordered pair of numbers to describe the position of points on a plane. This allows curves and lines to be described through algebraic equations, linking algebra and geometry. The coordinate plane is defined by perpendicular x and y axes that intersect at the origin. Points on the plane are located using their coordinates (x, y), marking their distance from the two axes. The plane is divided into four quadrants by the intersecting axes.
This document provides an introduction to coordinate geometry and the Cartesian coordinate system. It defines key terms like coordinates, quadrants, and plotting points. The Cartesian plane is formed by the intersection of the x and y axes, with the origin at (0,0). Any point can be uniquely identified using an ordered pair (x,y) representing the distances from the x and y axes. Examples are given of plotting points and calculating distances between points on the plane using their coordinates. In summary, the document outlines the basic concepts of the Cartesian coordinate system used in coordinate geometry.
History,applications,algebra and mathematical form of plane in mathematics (p...guesta62dea
The document provides information about planes and equations of planes. It defines a plane as a flat surface that extends indefinitely in width and height but has no thickness. Various plane shapes and their area formulas are described. Different forms of equations for a straight line including slope-intercept, point-slope, two-point, and standard forms are derived from the general linear equation. Two and three-dimensional Cartesian coordinate systems are also explained.
The rectangular coordinate system (also known as Cartesian plane) was developed by René Descartes and uses two perpendicular number lines (x-axis and y-axis) that intersect at the origin (0,0) to locate points in a plane. Any point is identified with an ordered pair (x,y) denoting its distances from the x-axis and y-axis. The axes divide the plane into four quadrants, and points can be plotted or identified from their coordinates.
The rectangular coordinate system (also known as the Cartesian plane) was developed by René Descartes and uses two perpendicular number lines (the x-axis and y-axis) that intersect at the origin (0,0) to locate points in a plane. Any point is identified with an ordered pair (x,y) denoting its distances from the x-axis and y-axis. The axes divide the plane into four quadrants, and points can be plotted or identified based on their coordinates.
Coordinate geometry represents points on a number line with real numbers. The number line places positive numbers to the right of zero and negative numbers to the left.
The Cartesian coordinate system uniquely determines points in two or three dimensional space using perpendicular x and y axes intersecting at the origin. René Descartes developed this system, linking algebra and geometry by describing curves and lines with equations.
The coordinate plane has perpendicular x and y axes. Points are located using their x and y coordinates, which represent horizontal and vertical distances from the origin. The plane is divided into four quadrants numbered counter-clockwise from the top right. Ordered pairs notation (x,y) specifies a point's location by listing the x coordinate first.
The document discusses key concepts about linear equations in two variables including:
1) It describes the Cartesian coordinate plane and how to plot points based on their x and y coordinates.
2) It explains how to find the slope, y-intercept, and x-intercept of a linear equation graphically and algebraically.
3) It provides examples of rewriting linear equations in slope-intercept form (y=mx+b) and using intercepts and slopes to graph lines on the coordinate plane.
Beginning direct3d gameprogrammingmath01_primer_20160324_jintaeksJinTaek Seo
This document provides an introduction to mathematics concepts for direct3D game programming, including:
- 2D rotation formulas for rotating a point about an angle
- Definitions of domain, codomain, exponentiation, factorial, square root, and cubic root
- Explanations of inverse functions, Pythagorean theorem, summation notation, and practice problems for various concepts
- Overviews of the Cartesian coordinate system, trigonometric functions, and how to implement them in programs
The document discusses coordinate geometry and the Cartesian coordinate system. It describes how René Descartes proposed using an ordered pair of numbers to describe the position of points on a plane. This allows curves and lines to be described through algebraic equations, linking algebra and geometry. The coordinate plane is defined by perpendicular x and y axes that intersect at the origin. Points on the plane are located using their coordinates (x, y), marking their distance from the two axes. The plane is divided into four quadrants by the intersecting axes.
The document discusses the Cartesian coordinate plane and its components. It defines the x-axis and y-axis, the origin point, quadrants, and coordinates. It also explains how to find the distance between two points using their coordinates. Finally, it provides information about circles, parabolas, and ellipses, including their definitions, key elements, and equations.
This document provides information about coordinate geometry and the Cartesian plane. It explains that coordinate geometry represents the position of objects in a plane using two perpendicular lines, known as axes. The system developed by René Descartes specifies each point using a pair of numerical coordinates representing the distance from the point to the two fixed axes. The axes divide the plane into four quadrants. Horizontal and vertical lines are designated relative to the axes and do not intersect each other.
Coordinate geometry describes the position of points on a plane using an ordered pair of numbers in a Cartesian coordinate system. French mathematician René Descartes developed this system in the 1600s. The system uses two perpendicular axes, the x-axis and y-axis, that intersect at the origin point (0,0). Values to the right of the origin on the x-axis and above the origin on the y-axis are positive, while values to the left and below are negative. Together the axes divide the plane into four quadrants. The document provides examples of finding the abscissa (x-coordinate) and ordinate (y-coordinate) of points, as well as answering questions to test understanding of coordinate geometry concepts.
The document discusses the Cartesian coordinate system. It explains that the system uses a horizontal and vertical number line that intersect at the origin (0,0) to locate points in space. Any point has coordinates written as an ordered pair (x,y) representing its distance from the x-axis and y-axis. The plane is divided into four quadrants based on whether the x and y values are positive or negative. Examples are given to demonstrate plotting points in the quadrants and identifying the axes.
Analytic geometry introduced in the 1630s by Descartes and Fermat uses algebraic equations to describe geometric figures on a coordinate system. It connects algebra and geometry by plotting points using a coordinate system with real number coordinates. This allows geometric shapes to be represented by algebraic equations which can be graphed. Key concepts include the Cartesian plane, slope, distance and midpoint formulas, and relationships between lines such as parallel, perpendicular and angles between lines based on their slopes.
1. The document introduces analytic geometry and its use of Cartesian coordinate systems to determine properties of geometric figures algebraically.
2. It defines key concepts like directed lines and rectangular coordinates, and explains how to find the distance between two points and the area of polygons using their coordinates.
3. Formulas are provided to calculate distances between horizontal, vertical and slanted line segments, as well as the area of triangles and general polygons from the coordinates of their vertices. Sample problems demonstrate applying these formulas.
The document discusses key concepts in Cartesian geometry including:
- The Cartesian plane is defined by two perpendicular number lines called the x-axis and y-axis intersecting at the origin point.
- Given two points P1(x1,y1) and P2(x2,y2) on the Cartesian plane, the midpoint formula can be used to find the point Pm that is equidistant from both points.
- Common curves that can be represented on the Cartesian plane include circles, parabolas, ellipses, and hyperbolas through their standard equation forms.
This document provides an overview of coordinate geometry. It begins by defining the Cartesian coordinate system, which uses an ordered pair of numbers to describe the position of points on a plane. It then discusses the four quadrants of the coordinate plane and explains how to find the coordinates of a point. Other topics covered include the distance formula, midpoint formula, section formula, and formulas for finding the area of triangles and determining collinearity of three points using coordinate geometry. Examples are provided to illustrate each concept. The document concludes by suggesting using coordinate geometry to mark landmarks on a city map.
The document discusses the Cartesian plane and its key elements. It describes how René Descartes originated the Cartesian plane by constructing two perpendicular number lines intersecting at a point. The document then defines the key parts of the Cartesian plane, including the x and y axes, quadrants, coordinates, and origin point. It also provides equations for circles, ellipses, hyperbolas, and parabolas in the Cartesian plane.
The document discusses the Cartesian plane and its key elements. It describes how René Descartes originated the Cartesian plane by constructing two perpendicular number lines intersecting at an origin point. The document then defines the key parts of the Cartesian plane, including the x and y axes, quadrants, coordinates, and how distance between points is calculated. It also provides the equations for circles, ellipses, hyperbolas, and parabolas - the main conic sections represented using the Cartesian plane.
Analytic geometry is a branch of mathematics that uses algebraic equations to describe geometric figures in a coordinate system. It was introduced in the 1630s by René Descartes and Pierre de Fermat and allowed for the development of modern mathematics and calculus by linking algebra and geometry. The central idea is using a coordinate system to relate geometric points to real numbers, allowing geometric figures to be described by algebraic equations.
Analytic geometry is a branch of mathematics that uses algebraic equations to describe geometric figures in a coordinate system. It was introduced in the 1600s by Descartes and Fermat and allowed geometry and algebra to be linked through coordinate systems. The Cartesian plane forms the basis of analytic geometry by allowing algebraic equations to be graphically represented through coordinate points and mapping geometric shapes like lines, circles, and conics to algebraic equations.
The document discusses geometric and analytical thinking. It begins by defining analytical geometry as the science that combines algebra and geometry to describe geometric figures from both algebraic and geometric viewpoints. It then discusses how analytical geometry originated with René Descartes' use of the Cartesian plane. Several geometric figures are then analyzed, including lines, circles, ellipses, and parabolas. Their key parameters and equations are defined. In particular, it provides the canonical equations for circles, ellipses, and parabolas, and discusses topics like slope and parallelism for lines.
This document discusses calculating the area under a curve using integration. It begins by approximating the area under an irregular shape using squares and rectangles. It then introduces defining the area A as a limit of approximating rectangles as their width approaches 0. This is written as the integral from a to b of f(x) dx, where f(x) is the curve. Examples are given of setting up definite integrals to calculate the areas under curves and between two curves. Steps for determining the area of a plane figure using integration are also provided.
This is a professional looking presentation on coordinate geometry By Rahul Bera. It has 10 pages You can edit the name and can change to another from Rahul Bera to yours.
The document provides a summary of coordinate geometry. It begins with definitions of key terms like the coordinate plane, axes, quadrants, and coordinates. It then discusses finding the midpoint, distance, and section formula between two points. Methods for finding the coordinates of the centroid and area of a triangle are presented. The document outlines different forms of equations for straight lines, including their slopes and the general equation of a line. It concludes with some uses of coordinate geometry, such as determining if lines are parallel/perpendicular.
This document provides information about coordinate grids, ordered pairs, and formulas in coordinate geometry. It defines key terms like coordinates, quadrants, and distance and section formulas. The distance formula calculates the distance between two points with coordinates (x1, y1) and (x2, y2). The section formula finds the coordinates of a point that divides a line segment between (x1, y1) and (x2, y2) in a given ratio. It also discusses finding the midpoint and calculating the area of a triangle using coordinates.
Coordinate geometry is a system that describes the position of points on a plane using ordered pairs of numbers. Rene Descartes developed this branch of mathematics in the 17th century. A coordinate plane has two perpendicular axes (x and y) that intersect at the origin point (0,0). The distance between any two points on the plane can be calculated using the Pythagorean theorem. Key concepts covered include finding the midpoint and points of trisection on a line segment, as well as using the section formula to determine the coordinates of a centroid.
Coordinate geometry is a system that describes the position of points on a plane using ordered pairs of numbers. Rene Descartes developed this branch of mathematics in the 17th century. A coordinate plane has two perpendicular axes (x and y) that intersect at the origin point (0,0). The distance between any two points on the plane can be calculated using the Pythagorean theorem. The midpoint and points of trisection of a line segment can be found using section formulas, as can the coordinates of the centroid of a figure.
The document discusses the Cartesian coordinate plane and its components. It defines the x-axis and y-axis, the origin point, quadrants, and coordinates. It also explains how to find the distance between two points using their coordinates. Finally, it provides information about circles, parabolas, and ellipses, including their definitions, key elements, and equations.
This document provides information about coordinate geometry and the Cartesian plane. It explains that coordinate geometry represents the position of objects in a plane using two perpendicular lines, known as axes. The system developed by René Descartes specifies each point using a pair of numerical coordinates representing the distance from the point to the two fixed axes. The axes divide the plane into four quadrants. Horizontal and vertical lines are designated relative to the axes and do not intersect each other.
Coordinate geometry describes the position of points on a plane using an ordered pair of numbers in a Cartesian coordinate system. French mathematician René Descartes developed this system in the 1600s. The system uses two perpendicular axes, the x-axis and y-axis, that intersect at the origin point (0,0). Values to the right of the origin on the x-axis and above the origin on the y-axis are positive, while values to the left and below are negative. Together the axes divide the plane into four quadrants. The document provides examples of finding the abscissa (x-coordinate) and ordinate (y-coordinate) of points, as well as answering questions to test understanding of coordinate geometry concepts.
The document discusses the Cartesian coordinate system. It explains that the system uses a horizontal and vertical number line that intersect at the origin (0,0) to locate points in space. Any point has coordinates written as an ordered pair (x,y) representing its distance from the x-axis and y-axis. The plane is divided into four quadrants based on whether the x and y values are positive or negative. Examples are given to demonstrate plotting points in the quadrants and identifying the axes.
Analytic geometry introduced in the 1630s by Descartes and Fermat uses algebraic equations to describe geometric figures on a coordinate system. It connects algebra and geometry by plotting points using a coordinate system with real number coordinates. This allows geometric shapes to be represented by algebraic equations which can be graphed. Key concepts include the Cartesian plane, slope, distance and midpoint formulas, and relationships between lines such as parallel, perpendicular and angles between lines based on their slopes.
1. The document introduces analytic geometry and its use of Cartesian coordinate systems to determine properties of geometric figures algebraically.
2. It defines key concepts like directed lines and rectangular coordinates, and explains how to find the distance between two points and the area of polygons using their coordinates.
3. Formulas are provided to calculate distances between horizontal, vertical and slanted line segments, as well as the area of triangles and general polygons from the coordinates of their vertices. Sample problems demonstrate applying these formulas.
The document discusses key concepts in Cartesian geometry including:
- The Cartesian plane is defined by two perpendicular number lines called the x-axis and y-axis intersecting at the origin point.
- Given two points P1(x1,y1) and P2(x2,y2) on the Cartesian plane, the midpoint formula can be used to find the point Pm that is equidistant from both points.
- Common curves that can be represented on the Cartesian plane include circles, parabolas, ellipses, and hyperbolas through their standard equation forms.
This document provides an overview of coordinate geometry. It begins by defining the Cartesian coordinate system, which uses an ordered pair of numbers to describe the position of points on a plane. It then discusses the four quadrants of the coordinate plane and explains how to find the coordinates of a point. Other topics covered include the distance formula, midpoint formula, section formula, and formulas for finding the area of triangles and determining collinearity of three points using coordinate geometry. Examples are provided to illustrate each concept. The document concludes by suggesting using coordinate geometry to mark landmarks on a city map.
The document discusses the Cartesian plane and its key elements. It describes how René Descartes originated the Cartesian plane by constructing two perpendicular number lines intersecting at a point. The document then defines the key parts of the Cartesian plane, including the x and y axes, quadrants, coordinates, and origin point. It also provides equations for circles, ellipses, hyperbolas, and parabolas in the Cartesian plane.
The document discusses the Cartesian plane and its key elements. It describes how René Descartes originated the Cartesian plane by constructing two perpendicular number lines intersecting at an origin point. The document then defines the key parts of the Cartesian plane, including the x and y axes, quadrants, coordinates, and how distance between points is calculated. It also provides the equations for circles, ellipses, hyperbolas, and parabolas - the main conic sections represented using the Cartesian plane.
Analytic geometry is a branch of mathematics that uses algebraic equations to describe geometric figures in a coordinate system. It was introduced in the 1630s by René Descartes and Pierre de Fermat and allowed for the development of modern mathematics and calculus by linking algebra and geometry. The central idea is using a coordinate system to relate geometric points to real numbers, allowing geometric figures to be described by algebraic equations.
Analytic geometry is a branch of mathematics that uses algebraic equations to describe geometric figures in a coordinate system. It was introduced in the 1600s by Descartes and Fermat and allowed geometry and algebra to be linked through coordinate systems. The Cartesian plane forms the basis of analytic geometry by allowing algebraic equations to be graphically represented through coordinate points and mapping geometric shapes like lines, circles, and conics to algebraic equations.
The document discusses geometric and analytical thinking. It begins by defining analytical geometry as the science that combines algebra and geometry to describe geometric figures from both algebraic and geometric viewpoints. It then discusses how analytical geometry originated with René Descartes' use of the Cartesian plane. Several geometric figures are then analyzed, including lines, circles, ellipses, and parabolas. Their key parameters and equations are defined. In particular, it provides the canonical equations for circles, ellipses, and parabolas, and discusses topics like slope and parallelism for lines.
This document discusses calculating the area under a curve using integration. It begins by approximating the area under an irregular shape using squares and rectangles. It then introduces defining the area A as a limit of approximating rectangles as their width approaches 0. This is written as the integral from a to b of f(x) dx, where f(x) is the curve. Examples are given of setting up definite integrals to calculate the areas under curves and between two curves. Steps for determining the area of a plane figure using integration are also provided.
This is a professional looking presentation on coordinate geometry By Rahul Bera. It has 10 pages You can edit the name and can change to another from Rahul Bera to yours.
The document provides a summary of coordinate geometry. It begins with definitions of key terms like the coordinate plane, axes, quadrants, and coordinates. It then discusses finding the midpoint, distance, and section formula between two points. Methods for finding the coordinates of the centroid and area of a triangle are presented. The document outlines different forms of equations for straight lines, including their slopes and the general equation of a line. It concludes with some uses of coordinate geometry, such as determining if lines are parallel/perpendicular.
This document provides information about coordinate grids, ordered pairs, and formulas in coordinate geometry. It defines key terms like coordinates, quadrants, and distance and section formulas. The distance formula calculates the distance between two points with coordinates (x1, y1) and (x2, y2). The section formula finds the coordinates of a point that divides a line segment between (x1, y1) and (x2, y2) in a given ratio. It also discusses finding the midpoint and calculating the area of a triangle using coordinates.
Coordinate geometry is a system that describes the position of points on a plane using ordered pairs of numbers. Rene Descartes developed this branch of mathematics in the 17th century. A coordinate plane has two perpendicular axes (x and y) that intersect at the origin point (0,0). The distance between any two points on the plane can be calculated using the Pythagorean theorem. Key concepts covered include finding the midpoint and points of trisection on a line segment, as well as using the section formula to determine the coordinates of a centroid.
Coordinate geometry is a system that describes the position of points on a plane using ordered pairs of numbers. Rene Descartes developed this branch of mathematics in the 17th century. A coordinate plane has two perpendicular axes (x and y) that intersect at the origin point (0,0). The distance between any two points on the plane can be calculated using the Pythagorean theorem. The midpoint and points of trisection of a line segment can be found using section formulas, as can the coordinates of the centroid of a figure.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
Physiology and chemistry of skin and pigmentation, hairs, scalp, lips and nail, Cleansing cream, Lotions, Face powders, Face packs, Lipsticks, Bath products, soaps and baby product,
Preparation and standardization of the following : Tonic, Bleaches, Dentifrices and Mouth washes & Tooth Pastes, Cosmetics for Nails.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
2. INDEX
INTRODUCTION
MAPPING THE PLANE
DISTANCE BETWEEN TWO POINTS
PROPERTIES OF DISTANCE
MIDPOINT OF A LINE SEGMENT
3. INTRODUCTION
The French Mathematician Rene Descartes developed
a new branch of Mathematics known as Analytical
Geometry or Coordinate Geometry.
Coordinate geometry (or analytic geometry) is defined
as the study of geometry using the coordinate points.
Using coordinate geometry, it is possible to find the
distance between two points, dividing lines in m:n
ratio, finding the mid-point of a line, calculating the
area of a triangle in the Cartesian plane, etc.
4. MAPPING THE PLANE
Draw a perpendicular line and mark X-axis and Y-axis.
In horizontal line the positive numbers lie on right side of
zero and negative numbers on left side of the zero.
In vertical line the positive numbers lie above zero and the
negative numbers lie below zero.
The x co-ordinate is called the Abscissa and the y co-
ordinate is called the Ordinate.
The X and Y axis divides the plane into four regions , they
are called as Quadrants.
5.
6. Plot ( -4 , -2 )
To plot the points (-4,-2) in the Cartesian coordinate plane. We
follow the x-axis until we reach -4 and draw a vertical line at x = -4
Similarly follow the y-axis until we reach -2 and draw a horizontal
line at y = -2
7. DISTANCE BETWEEN THE TWO POINTS
Distance between two points is the length
of the line segment that connects the two points in a plane.
The formula to find the distance between the two points is
usually given by d=√((x2 – x1)² + (y2 – y1)²).
10. MIDPOINT OF A LINE
SEGMENT
The midpoint of a segment is the point on the segment
that is equidistant from the endpoints.
In the above diagram,
B is the midpoint of A and C.