Rectangular coordinate system
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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.
Rectangular coordinate system
- 1. Chapter IV: Linear Equation in Two Variables
- 2. 4.1 Rectangular Coordinate System 4.2 Linear Equation in Two Variables 4.3 Relation and Function 4.4 Graphing Linear Equations 4.5 Writing Equations of Lines
- 4. Objectives: Define terms related to rectangular coordinate system; Value the importance of René Descartes works in plotting points; and Locate and plot points on the rectangular coordinate system.
- 5. Exploration: The seat plan of Section I-A prepared by Mr. Santos, the adviser, is shown below. Gail Ryan Sophia Danielle Ariel Shaila Connie Rose Faye Sedrick Johanna John Carl Paula Alcas Denisse Jobelle Carla Ayie Aaron Jerome Kirsten Alice Edward Rubie Aida Veilant Brian Ben Nina Mae Jacob Gerald Gertude Xavier Teacher’s Table Cathy
- 6. Exploration: Gail ______ Ariel (1 , 4) Rose ______ Sedrick ______ Gerald ______ Ryan ______ Shaila ______ Faye ______ Johanna (2 , 2) Gertude ______ Teacher’s Table Sophia ______ Connie ______ Ayie ______ Edward ______ Xavier ______ Danielle ______ Alcas ______ Aaron (4 , 3) Rubie ______ Ben ______ Cathy ______ Denisse ______ Jerome ______ Aida ______ Nina ______ John Carl (6 , 5) Jobelle ______ Kirsten ______ Veilant ______ Mae ______ Paula ______ Carla ______ Alice ______ Brian ______ Jacob (7 , 1)
- 7. Exploration: Gail Ryan (1 , 5) (2 , 5) Ariel Shaila (1 , 4) (2 , 4) Rose Faye (1 , 3) (2 , 3) Sedrick Johanna (2 , 2) (1 , 2) Gerald Gertude (1 , 1) (2 , 1) Teacher’s Table Sophia Danielle Cathy John Carl (6 , 5) (3 , 5) (4 , 5) (5 , 5) Connie Alcas Denisse Jobelle (3 , 4) (4 , 4) (5 , 4) (6 , 4) Ayie Aaron Jerome Kirsten (3 , 3) (4 , 3) (5 , 3) (6 , 3) Edward Rubie Aida Veilant (3 , 2) (4 , 2) (5 , 2) (6 , 2) Xavier Ben Nina Mae (3 , 1) (4 , 1) (5 , 1) (6 , 1) Paula (7 , 5) Carla (7 , 4) Alice (7 , 3) Brian (7 , 2) Jacob (7 , 1)
- 8. QUESTIONS: Can you see any pattern in the number pairs written against each student’s name done by Mr. Cruz? Describe the pattern. Did Mr. Cruz use the pairs of numbers (2 , 3) and (3 , 2) to refer to the same seat? If not, who occupied the seat numbered (2 , 3) and (3 , 2)?
- 9. Cartesian Plane or x-y Plane A Cartesian Plane or x-y Plane (in honor of Rene Descartes) is made up of two perpendicular number lines (coordinate axes), one is horizontal (x-axis) and the other is vertical (y-axis), whose point of intersection is called the origin. The horizontal line is called the x-axis or the abscissa and the vertical line is called the y-axis or the ordinate. The two axes divide the plane into four area called as quadrants that are numbered in a counterclockwise direction.
- 10. RENÉ DESCARTES René Descartes (1596-1650) is a French mathematician, philosopher, and theologian. He was brilliant but sickly. Thus, his teachers allowed him to lie in bed in the morning for rest and reflection. He came up with many of his philosophical and mathematical ideas during his morning meditations, a practice which he continued throughout his life.
- 11. RENÉ DESCARTES Sometimes the same thing that makes one person bitter makes another better. René Descartes, being sickly, could have resigned himself to a less remarkable, even miserable life. Instead, he used those times in his sick bed to reflect on life and mathematical relationships, thereby making some of the most profound discoveries in mathematics. Reflect on your life. Is there a “liability” in your life that you could turn into an asset? What is it?
- 12. Locate the point (2 , 3)
- 13. To graph or plot a point given its coordinates: 1. Begin at the origin (0 , 0), move to the right or left along the x-axis using the number indicated by the absolute value of the first coordinate. 2. From that position on the x-axis, move up or down using the number indicated by the absolute value of the second coordinate. 3. Draw a dot to represent the point described by the coordinates.
- 14. To determine the coordinates of a point in the rectangular system: 1. Draw a vertical line passing through the point and the x-axis. The number associated to the point on the x-axis is the first coordinate. 2.Draw a horizontal line passing through the point and the y-axis. The number associated to the point on the y-axis is the second coordinate.
- 15. Assignment: 1. Study: Rectangular Coordinate System (illustrative examples 2 and 3) 2. Answer the following questions: a.If you are to plot (5 , 2) on the Cartesian plane without actually plotting, where do you think will the point lie? Give other points that will be located on the same region. What do you notice? Make a generalization. b.How is the signs of the coordinates affect the location of the point in the plane? Explain. c. Does (0 , -1) lie on any of the quadrant? Explain.
- 16. References: e – Math 8 (K-to-12 Edition) by Oronce et.al., page 127-131, 135 Intermediate Algebra (Explorations and Applications) by Gladys Nivera, page 119-124 http://www.math-aids.com/Graphing/ http://www.worksheetworks.com/math/geometry/ graphing.html
- 17. Thank You That in all things, God may be Glorified!!!