cartesian plane.pptx for grade 8 students
- 1. A Rectangular Coordinate System or also known as a Cartesian plane is named after the French mathematician René Descartes (1596 – 1650), who is known as the “Father of Modern Mathematics”. It is composed of two perpendicular number lines, typically called the − 𝑥 𝑎𝑥𝑖𝑠 and the − 𝑦 𝑎𝑥𝑖𝑠, respectively, that meet at a point of origin (0, 0) and divide the plane into four regions called quadrants which are numbered in sequence as Quadrant I, Quadrant II, Quadrant III, and Quadrant IV moving in a counter-clockwise direction starting from the upper right. RECTANGULAR COORDINATE SYSTEM
- 2. The horizontal number line is called the − . The vertical number line is called the − . 𝒙 𝒂𝒙𝒊𝒔 𝒚 𝒂𝒙𝒊𝒔 The point of intersection of the horizontal and vertical number lines is called the origin. Each point in the plane can be located using an ordered pair of numbers ( , ), 𝑥 𝑦 where 𝑥 is the horizontal distance and 𝑦 is the vertical distance of the point from the origin. The numbers in the ordered pair are called coordinates. The − of the coordinates ( , ) of a 𝑥 𝑣𝑎𝑙𝑢𝑒 𝑥 𝑦 point is also known as the abscissa, while the − is known as the 𝑦 𝑣𝑎𝑙𝑢𝑒 ordinate.
- 3. QUADRANTS IN A COORDINATE PLANE There are also points which lie in − − . The points which 𝑡ℎ𝑒 𝑥 𝑎𝑛𝑑 𝑦 𝑎𝑥𝑒𝑠 lie in the − have coordinates ( , 0) and the points which lie in the 𝑥 𝑎𝑥𝑖𝑠 𝑥 𝑦 − have coordinates (0, ), w 𝑎𝑥𝑖𝑠 𝑦
- 4. POINT L (3,4) means that the point is located 3 units to the right of the y-axis and 4 units above the x –axis. Since the signs of the coordinates are both positive, point L is in Quadrant I. POINT O (−3, 4) means that the point is located 3 units to the left of the y-axis and 4 units above the x-axis. Since the sign of the x-coordinate or the abscissa is negative and the sign of the y-coordinate or the ordinate is positive, then point O is in Quadrant II. POINT V (−3, −4) means that the point is located 3 units to the left of the y-axis and 4 units below the x-axis. Since the signs of both x-and y- coordinates are both negative, point V is in Quadrant III. POINT E (3, −4) means that the point is located 3 units to the right of the y-axis and 4 units below the x-axis. Since the sign of the x-coordinate or abscissa is positive and the sign of the y-coordinate or ordinate is negative, point E is in Quadrant IV.
- 5. Activity #2.2 Rectangular Coordinate System Get ¼ sheet of paper, read and answer the following. ANSWERS ONLY 1. He is the person behind the coordinate plane. 2. It is a horizontal number line in a coordinate plane. 3. It is a vertical number line in a coordinate plane. 4. The point of intersection of two number lines in a plane. 5. A set of two values as a coordinates. 6. The x – coordinate is also called ? 7. The y – coordinate is also called ? 8. It is the division of plane into four equal regions by intersection of x and y axis. 9. What quadrant does (-3 , -2) lie? 10. What quadrant does (0, 2) lie?
- 6. Activity #2.3 Coordinate Grid Picture Using a grid paper, make a Cartesian plane and plot the following points. Then, connect a line to create a diagram. (1,-3) (5,-4) (4,-3) (9,1) (7,2) (8,5) (5,4) (5,5) (3,4) (4,9) (2,7) (0,10) (-2,7) (-4,8) (-3,3) (-5,6) (-5,4) (-8,5) (-7,2) (-9,1) (-4,-3) (-5,-4) (0,-3) (2,-7) (2,-6) (1,-3)