CARTESIAN PLANE.pptx
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The document discusses the Cartesian coordinate system, which was created by René Descartes. It is a system that uses perpendicular x and y axes to uniquely identify points in a plane by their coordinates. Examples are given of plotting points and finding the area of a rectangle using this coordinate system. The key parts of the Cartesian plane like the quadrants and axes are identified. Exercises involving the coordinate system are provided from a textbook.
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Cartesian Coordinate Plane
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
Cartesian coordinate plane
The document discusses the Cartesian coordinate plane and functions. It defines the Cartesian plane as being formed by two perpendicular number lines called the x-axis and y-axis that intersect at the origin (0,0). It describes how each point on the plane is associated with an ordered pair (x,y) denoting its coordinates and how the plane is divided into four quadrants. It then demonstrates how to plot various points on the plane by starting at the origin and moving right or left along the x-axis and up or down along the y-axis. Finally, it discusses relations and functions, defining a function as a relation where each x-value is mapped to only one y-value.
cartesiancoordinateplane-140804022012-phpapp01.pdf
The document discusses the Cartesian coordinate plane and functions. It defines the Cartesian plane as being formed by two perpendicular number lines called the x-axis and y-axis that intersect at the origin point (0,0). Each point on the plane is represented by an ordered pair (x,y) denoting its coordinates. A relation is a set of ordered pairs while a function is a relation where each x-value is mapped to only one y-value. The document provides examples of relations, tables, and mappings to illustrate these concepts.
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This document discusses key concepts related to the rectangular coordinate system:
- It aims to summarize concepts of the Cartesian plane, explain its real-life uses, and demonstrate its representation through shapes and maps.
- It reviews plotting points on the Cartesian plane by providing examples of completing sentences with the correct coordinate system terms like axes, quadrants, and ordered pairs.
- It explains how to identify the quadrant a point is located in based on the signs of its x- and y-coordinates.
- It poses assignment questions about linear equations in two variables, including how to determine if an ordered pair is a solution to such an equation.
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The document discusses graphing ordered pairs on a coordinate plane. It defines key terms like coordinate, plane, axes, quadrants, and ordered pairs. It explains that the x-axis is horizontal, the y-axis is vertical, and they intersect at the origin (0,0). Ordered pairs use the format (x,y) to locate points by giving the x-coordinate first and y-coordinate second. Several examples are given to demonstrate graphing points in the quadrants of the coordinate plane.
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The document discusses graphing ordered pairs on a coordinate plane. It defines key terms like coordinate, plane, axes, quadrants, and ordered pairs. It explains that an ordered pair uses the format (x,y) to locate a point by its x-coordinate first and then y-coordinate on the plane. Several examples of graphing points and identifying their quadrants are provided.
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Cartesian Coordinate Plane
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
Cartesian coordinate plane
The document discusses the Cartesian coordinate plane and functions. It defines the Cartesian plane as being formed by two perpendicular number lines called the x-axis and y-axis that intersect at the origin (0,0). It describes how each point on the plane is associated with an ordered pair (x,y) denoting its coordinates and how the plane is divided into four quadrants. It then demonstrates how to plot various points on the plane by starting at the origin and moving right or left along the x-axis and up or down along the y-axis. Finally, it discusses relations and functions, defining a function as a relation where each x-value is mapped to only one y-value.
cartesiancoordinateplane-140804022012-phpapp01.pdf
The document discusses the Cartesian coordinate plane and functions. It defines the Cartesian plane as being formed by two perpendicular number lines called the x-axis and y-axis that intersect at the origin point (0,0). Each point on the plane is represented by an ordered pair (x,y) denoting its coordinates. A relation is a set of ordered pairs while a function is a relation where each x-value is mapped to only one y-value. The document provides examples of relations, tables, and mappings to illustrate these concepts.
Rectangular Coordinate System II
This document discusses key concepts related to the rectangular coordinate system:
- It aims to summarize concepts of the Cartesian plane, explain its real-life uses, and demonstrate its representation through shapes and maps.
- It reviews plotting points on the Cartesian plane by providing examples of completing sentences with the correct coordinate system terms like axes, quadrants, and ordered pairs.
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- It poses assignment questions about linear equations in two variables, including how to determine if an ordered pair is a solution to such an equation.
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References are from Google.com.
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The document discusses graphing ordered pairs on a coordinate plane. It defines key terms like coordinate, plane, axes, quadrants, and ordered pairs. It explains that an ordered pair uses the format (x,y) to locate a point by its x-coordinate first and then y-coordinate on the plane. Several examples of graphing points and identifying their quadrants are provided.
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The document describes the rectangular coordinate system and how to plot points on a Cartesian plane. It discusses the key elements of the system, including the x-axis, y-axis, origin, and quadrants. It also provides steps for plotting points based on their x- and y-coordinates and examples of determining the quadrant that points are located in.
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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.
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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.
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This document provides information about the Cartesian coordinate system developed by René Descartes, including:
- It consists of two perpendicular number lines (axes) that intersect at their zero point (origin).
- The x-axis is horizontal and the y-axis is vertical.
- Points on the plane are represented by an ordered pair (x, y) called coordinates, where x is the x-coordinate (abscissa) and y is the y-coordinate (ordinate).
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1. René Descartes lay in bed one night and noticed a fly on his ceiling, which inspired him to develop a way to precisely describe locations using coordinates.
2. He devised a system using two perpendicular lines intersecting at right angles, with numbers along each line to specify locations as ordered pairs of numbers.
3. This Cartesian coordinate system, which places locations on a Cartesian plane using x and y values, allowed Descartes to precisely describe the location of the fly as (4,5).
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The document introduces concepts related to the coordinate plane, including the x-axis, y-axis, origin, quadrants, ordered pairs, and graphing points. It explains that the x-axis is horizontal, the y-axis is vertical, and the origin is at the center point (0,0). Points can fall into four quadrants depending on whether their x and y values are positive or negative. An example point (-5,3) is shown to lie in Quadrant II. The coordinates of two points A and B are given as (-5,-7) and (7,-2).
Module 4 topic 1 part 1 notes
The document introduces concepts related to the coordinate plane, including the x-axis, y-axis, origin, quadrants, ordered pairs, and graphing points. It explains that the x-axis is horizontal, the y-axis is vertical, and the origin is at the center point (0,0). Points can fall into four quadrants depending on whether their x and y values are positive or negative. An example point (-5,3) is shown to lie in Quadrant II. The coordinates of two points A and B are given as (-5,-7) and (7,-2).
G6 m3-c-lesson 15-t
This lesson teaches students about locating ordered pairs on the coordinate plane:
- It reviews extending the x-axis and y-axis to include negative numbers, dividing the plane into four quadrants.
- Students learn to identify the origin and locate points on the axes or in the quadrants by their ordered pair coordinates.
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MA1310 Week 6 Polar Coordinates and Complex NumbersThis lab req.docx
MA1310: Week 6 Polar Coordinates and Complex Numbers
This lab requires you to:
· Plot points in the polar coordinate system.
· Find multiple sets of polar coordinates for a given system.
· Convert a point from polar to rectangular coordinates.
· Convert a point from rectangular to polar coordinates.
· Plot complex numbers in the complex plane.
· Find the absolute value of a complex number.
· Write complex numbers in polar form.
· Convert a complex number from polar form to rectangular form.
· Find products of complex numbers in polar form.
· Find quotients of complex numbers in polar form.
· Find powers of complex numbers in polar form (DeMoivre's Theorem).
Answer the following questions to complete this lab:
1.
Explain why and represent the same points in polar coordinates.
2.
Match the point in polar coordinates with either A, B, C, or D on the graph.
3.
Find the rectangular coordinates of the polar point.
4. Find the polar coordinates of the rectangular point (–4, –4).
5.
Plot the complex number.
a.
b.
c.
d.
6. Find the absolute value of the complex number z = 2 + 5i.
7.
Write the complex number z = 2 – 2i in polar form. Express in degrees.
8.
Write the complex number in rectangular form.
9. Use DeMoivre's Theorem to find the indicated power of the complex number. Write answer in rectangular form.
Submission Requirements: Answer all the questions included in the lab. You can submit your answers in a Microsoft Word document, or write your answers on paper and then scan and submit the paper. Name the file as InitialName_LastName_Lab6.1_Date.
Evaluation Criteria:
· Did you show the appropriate steps to solve the given problems?
· Did you support your answers with appropriate rationale wherever applicable?
· Were the answers submitted in an organized fashion that was legible and easy to follow?
· Were the answers correct?
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Running head: TITTLE 1
Abstract
TITTLE 13
Tittle
Level One header
Level One header
Level one header
Conclusion
References
...
PPTs FOR 9TH CLASS COORDINATE GEOMETRY INTRODUCTION C
This document introduces coordinate geometry and the Cartesian plane. It explains that René Descartes developed a method to describe the position of a point in a plane using two perpendicular lines as axes. Any point can be located using its distance from these intersecting x- and y-axes, known as the point's coordinates. The plane is divided into four quadrants by the axes, and examples are provided to demonstrate how to locate a point using its coordinates.
CYCLIC PERMUTATION.pptx
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PROBABILITY.pptx
This document discusses probability and compound events. It defines key probability terms like experiment, outcomes, sample space, and events. It also covers unions and intersections of events. Examples are provided to illustrate finding the union and intersection of events. The document concludes with assignments, including answering practice problems on unions and intersections of events, and generating additional problems involving the probability of compound events.
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This document provides an overview of linear equations in two variables and the rectangular coordinate system. It defines key terms like the x-axis, y-axis, and quadrants. It describes how René Descartes developed the coordinate plane and revolutionized mathematics. The document explains how to locate and plot points on the plane using x and y coordinates. It includes examples of plotting points and determining the coordinates of points. Students are assigned questions about plotting points in different quadrants and how the signs of coordinates affect a point's location.
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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.
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The document describes Cartesian planes and number planes. A Cartesian plane specifies each point uniquely using a pair of numerical coordinates representing the signed distances from the point to two fixed perpendicular lines. The number plane consists of all ordered pairs of real numbers plotted on an x-axis and y-axis, with the point of intersection called the origin. The plane is divided into four quadrants.
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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.
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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.
New approaches in linear inequalities
This lesson teaches students how to graph and solve systems of linear inequalities on a coordinate plane. It begins by reviewing how to graph single linear inequalities and shade the correct region. Students then learn that a system involves graphing two or more inequalities on the same plane. The solution region is where the shading overlaps - where all inequalities are simultaneously satisfied. Students practice graphing systems with two, three and four inequalities, and interpreting the solution region where shading coincides. The lesson concludes by challenging students to locate treasure using coordinates satisfying a given system of inequalities.
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The document discusses the rectangular coordinate system and plotting points on a Cartesian plane. It begins by stating the objectives of understanding the rectangular coordinate system, plotting points, and completing tasks cooperatively. Classroom policies for discussions are outlined. A motivation activity called the "Row-Column Game" is described to call on students by row and column to answer questions about a seating chart. Concepts of the rectangular coordinate system like quadrants, axes, and ordered pairs are analyzed. The history of the system developed by René Descartes is provided. Examples are given to illustrate plotting points and connecting the rectangular coordinate system to real-life and other subjects. An assignment requires students to plot locations on a Cartesian plane and connect the points to form an object
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This document provides information about the Cartesian coordinate system developed by René Descartes, including:
- It consists of two perpendicular number lines (axes) that intersect at their zero point (origin).
- The x-axis is horizontal and the y-axis is vertical.
- Points on the plane are represented by an ordered pair (x, y) called coordinates, where x is the x-coordinate (abscissa) and y is the y-coordinate (ordinate).
coordinategeometryppt-180912064900.pptx
1. René Descartes lay in bed one night and noticed a fly on his ceiling, which inspired him to develop a way to precisely describe locations using coordinates.
2. He devised a system using two perpendicular lines intersecting at right angles, with numbers along each line to specify locations as ordered pairs of numbers.
3. This Cartesian coordinate system, which places locations on a Cartesian plane using x and y values, allowed Descartes to precisely describe the location of the fly as (4,5).
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The document introduces concepts related to the coordinate plane, including the x-axis, y-axis, origin, quadrants, ordered pairs, and graphing points. It explains that the x-axis is horizontal, the y-axis is vertical, and the origin is at the center point (0,0). Points can fall into four quadrants depending on whether their x and y values are positive or negative. An example point (-5,3) is shown to lie in Quadrant II. The coordinates of two points A and B are given as (-5,-7) and (7,-2).
Module 4 topic 1 part 1 notes
The document introduces concepts related to the coordinate plane, including the x-axis, y-axis, origin, quadrants, ordered pairs, and graphing points. It explains that the x-axis is horizontal, the y-axis is vertical, and the origin is at the center point (0,0). Points can fall into four quadrants depending on whether their x and y values are positive or negative. An example point (-5,3) is shown to lie in Quadrant II. The coordinates of two points A and B are given as (-5,-7) and (7,-2).
G6 m3-c-lesson 15-t
This lesson teaches students about locating ordered pairs on the coordinate plane:
- It reviews extending the x-axis and y-axis to include negative numbers, dividing the plane into four quadrants.
- Students learn to identify the origin and locate points on the axes or in the quadrants by their ordered pair coordinates.
- Exercises have students graph points, identify quadrants, and note properties of points based on their coordinates.
MA1310 Week 6 Polar Coordinates and Complex NumbersThis lab req.docx
MA1310: Week 6 Polar Coordinates and Complex Numbers
This lab requires you to:
· Plot points in the polar coordinate system.
· Find multiple sets of polar coordinates for a given system.
· Convert a point from polar to rectangular coordinates.
· Convert a point from rectangular to polar coordinates.
· Plot complex numbers in the complex plane.
· Find the absolute value of a complex number.
· Write complex numbers in polar form.
· Convert a complex number from polar form to rectangular form.
· Find products of complex numbers in polar form.
· Find quotients of complex numbers in polar form.
· Find powers of complex numbers in polar form (DeMoivre's Theorem).
Answer the following questions to complete this lab:
1.
Explain why and represent the same points in polar coordinates.
2.
Match the point in polar coordinates with either A, B, C, or D on the graph.
3.
Find the rectangular coordinates of the polar point.
4. Find the polar coordinates of the rectangular point (–4, –4).
5.
Plot the complex number.
a.
b.
c.
d.
6. Find the absolute value of the complex number z = 2 + 5i.
7.
Write the complex number z = 2 – 2i in polar form. Express in degrees.
8.
Write the complex number in rectangular form.
9. Use DeMoivre's Theorem to find the indicated power of the complex number. Write answer in rectangular form.
Submission Requirements: Answer all the questions included in the lab. You can submit your answers in a Microsoft Word document, or write your answers on paper and then scan and submit the paper. Name the file as InitialName_LastName_Lab6.1_Date.
Evaluation Criteria:
· Did you show the appropriate steps to solve the given problems?
· Did you support your answers with appropriate rationale wherever applicable?
· Were the answers submitted in an organized fashion that was legible and easy to follow?
· Were the answers correct?
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--
ç÷
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5,
2
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434
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33
6cossin
22
i
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5
1
cossin
41010
i
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pp
æö
+
êú
ç÷
èø
ëû
(,)
r
q
Running head: TITTLE 1
Abstract
TITTLE 13
Tittle
Level One header
Level One header
Level one header
Conclusion
References
...
PPTs FOR 9TH CLASS COORDINATE GEOMETRY INTRODUCTION C
This document introduces coordinate geometry and the Cartesian plane. It explains that René Descartes developed a method to describe the position of a point in a plane using two perpendicular lines as axes. Any point can be located using its distance from these intersecting x- and y-axes, known as the point's coordinates. The plane is divided into four quadrants by the axes, and examples are provided to demonstrate how to locate a point using its coordinates.
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RECTANGULAR COORDINATE SYSTEM CLASSROOM OBSERVATION.pptx
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This document discusses probability of simple events. It defines key terms like outcome, sample space, simple event and complementary events. It provides examples of calculating probability for events like rolling dice, spinning a spinner or flipping a coin. The probability of an event is defined as the number of favorable outcomes divided by the total number of possible outcomes. Students are given examples to practice calculating probabilities and real world scenarios are provided to demonstrate applications of probability.
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Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
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2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
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- 3. • What do you call the figure on the screen? • Can anyone identify the different parts of the figure? How can we use it?
- 5. • Also known as Cartesian coordinate system named after the famous French philosopher and mathematician Rene Descartes. It is a system coordinate axes.
- 10. Examples Example: • An ordered pair (4, 5) represents point 4 units to the right of the origin in the direction of the x-axis, and 5 units above the origin in the direction of the y-axis as shown in the diagram below.
- 11. Example: • Plot the point (–5, 4) and identify which quadrant or axis it is located.
- 12. •Sketch rectangle ABCD with the given vertices and find its area. 𝐴 −2, −3 , 𝐵 5, −3 , 𝐶(5,4), 𝐷(−2,4)
- 13. Give the parts of a Cartesian coordinate Plane
- 14. Examples
- 15. Answer: Solve the exercises on Rectangular Coordinate System on p.166-167
- 17. “I think; therefore I am.” - René Descartes
- 19. Answer POWERPLUS page 18 (Letters B-C only).