coordinate geometry.pptx
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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.
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Coordinate geometry
Coordinate geometry describes the position of points on a plane using an ordered pair of numbers (x, y). It was developed by French mathematician René Descartes 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 x-axis and above the y-axis are positive, while values to the left and below are negative. The plane is divided into four quadrants by these axes.
COORDINATE Geometry.pptx
Coordinate geometry describes the position of points in a plane using perpendicular x and y axes that intersect at the origin. The French mathematician Rene Descartes developed this Cartesian coordinate system. A point's position is defined by its x-coordinate (distance from the y-axis) and y-coordinate (distance from the x-axis). The four quadrants formed by dividing the plane with the x and y axes determine the signs of the coordinates.
Co-ordinate Geometry.pptx
Introduction to Co-ordinate Geometry
Mapping the plane
Distance between two points
Distance formula
Properties of distance
Midpoint of a line segment
Midpoint formula
The rectangular coordinate plane
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.
Co ordinate geometry done
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.
cartesian plane by : joe olivare
This document provides information about the Cartesian plane (or Cartesian coordinate system) including:
- It specifies each point uniquely using a pair of numerical coordinates that represent the distance from the point to two fixed perpendicular axes.
- Rene Descartes invented the Cartesian coordinate system to plot ordered pairs (x,y) on a plane with perpendicular x and y axes intersecting at the origin (0,0).
- The x-coordinate represents the horizontal axis and the y-coordinate represents the vertical axis. Ordered pairs written as (x, y) locate a point by moving left/right along the x-axis and up/down along the y-axis from the origin.
Coordinate geometry
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.
Coordinate goemetry
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.
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Coordinate geometry
Coordinate geometry describes the position of points on a plane using an ordered pair of numbers (x, y). It was developed by French mathematician René Descartes 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 x-axis and above the y-axis are positive, while values to the left and below are negative. The plane is divided into four quadrants by these axes.
COORDINATE Geometry.pptx
Coordinate geometry describes the position of points in a plane using perpendicular x and y axes that intersect at the origin. The French mathematician Rene Descartes developed this Cartesian coordinate system. A point's position is defined by its x-coordinate (distance from the y-axis) and y-coordinate (distance from the x-axis). The four quadrants formed by dividing the plane with the x and y axes determine the signs of the coordinates.
Co-ordinate Geometry.pptx
Introduction to Co-ordinate Geometry
Mapping the plane
Distance between two points
Distance formula
Properties of distance
Midpoint of a line segment
Midpoint formula
The rectangular coordinate plane
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.
Co ordinate geometry done
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.
cartesian plane by : joe olivare
This document provides information about the Cartesian plane (or Cartesian coordinate system) including:
- It specifies each point uniquely using a pair of numerical coordinates that represent the distance from the point to two fixed perpendicular axes.
- Rene Descartes invented the Cartesian coordinate system to plot ordered pairs (x,y) on a plane with perpendicular x and y axes intersecting at the origin (0,0).
- The x-coordinate represents the horizontal axis and the y-coordinate represents the vertical axis. Ordered pairs written as (x, y) locate a point by moving left/right along the x-axis and up/down along the y-axis from the origin.
Coordinate geometry
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.
Coordinate goemetry
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.
CO-ORDINATE GEOMETRY
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
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.
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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.
Coordinate System.pptx
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.
Cartesian coordinates
Cartesian coordinates use a grid system to precisely locate points in space. A point is identified by its x and y coordinates, which indicate the distance from the origin point along the x-axis and y-axis. For example, the point (3,2) is located 3 units to the right of the origin along the x-axis and 2 units above the origin along the y-axis. The axes divide the plane into four quadrants, with points falling into different quadrants based on whether their x and y values are positive or negative. Cartesian coordinates provide a way to pinpoint locations using simple numbers.
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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.
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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.
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The rectangular coordinate system consists of two number lines that intersect perpendicularly to form an x-axis and y-axis, defining a plane where each point is associated with an ordered pair of real numbers (x,y). The x-coordinate is the number where the point intersects the horizontal x-axis and the y-coordinate is the number where it intersects the vertical y-axis, with the point of intersection being the origin (0,0).
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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.
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René Descartes is credited with developing the Cartesian plane by joining algebra and geometry. The Cartesian plane is formed by intersecting two perpendicular number lines, called the x-axis and y-axis, dividing the plane into four quadrants. Each point on the Cartesian plane is associated with an ordered pair of coordinates (x,y) representing its distance from the origin, where the axes intersect.
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The rectangular coordinate system, also known as the Cartesian coordinate system, was developed by the French mathematician René Descartes. It uses two perpendicular number lines, the x-axis and y-axis, that intersect at the origin (0,0) to locate points in a plane. Each point is identified with an ordered pair of numbers known as Cartesian coordinates that represent the distance from the origin on the x-axis and y-axis. The system divides the plane into four quadrants and allows points to be easily plotted and located.
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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.
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Rene Descartes invented the Cartesian coordinate system in the 17th century. The Cartesian plane is a two-dimensional graph with perpendicular x and y axes that intersect at the origin. Any point on the plane is identified with an ordered pair (x, y) denoting its distances from the x and y axes. Examples show how to locate points in the four quadrants based on their x and y values and determine which quadrant they fall in.
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René Descartes was a 17th century French philosopher, mathematician, and scientist. He is considered the father of modern western philosophy and developed Cartesian coordinate system to represent geometric lines and curves with algebraic equations. The Cartesian coordinate system uses two perpendicular axes (x and y axes) intersecting at the origin to determine the position of a point in a plane.
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Okay, here are the steps to solve this problem:
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Rene Descartes invented the Cartesian coordinate system in the 17th century. The Cartesian plane is a two-dimensional graph with perpendicular x and y axes that intersect at the origin. Any point on the plane is identified with an ordered pair (x, y) denoting its distances from the x and y axes. Examples show how to locate points in the four quadrants based on their x and y values and determine which quadrant they fall in.
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René Descartes was a 17th century French philosopher, mathematician, and scientist. He is considered the father of modern western philosophy and developed Cartesian coordinate system to represent geometric lines and curves with algebraic equations. The Cartesian coordinate system uses two perpendicular axes (x and y axes) intersecting at the origin to determine the position of a point in a plane.
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Okay, here are the steps to solve this problem:
1) The sphere has a radius of 8 inches
2) To find the volume of a sphere we use the formula: V = (4/3)πr^3
3) Plugging in the values:
V = (4/3)π(8)^3
V = (4/3)π(512)
V = 1024π
So the volume of the spherical fish tank with a radius of 8 inches is 1024π cubic inches.
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Primes Factor Trees.ppt
This document defines key terms related to prime and composite numbers including: product, factor, prime number, composite number, and prime factorization. It provides examples of prime numbers (numbers with exactly two factors) such as 2, 3, 5, 7, and examples of composite numbers (numbers with more than two factors) such as 4, 6, 8, 9. The document explains how to perform prime factorization by writing a composite number as a product of prime factors using a factor tree method in multiple steps. It provides examples of prime factoring various numbers between 4 and 22.
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- 1. COORDINATE GEOMETRY Class 9 Prepared by: SHARDA CHAUHAN TGT MATHEMATICS
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- 3. French Mathematician René Descartes (1596 - 1650).
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- 10. X- axis O Y- axis Y- axis 1. On Y- axis 2. In the IVth quadrant X. axis 3. In the IInd quadrant 4. On X- axis
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