2The year is Lying on his back, French mathematician René Descartes, watches a fly crawl across the ceiling. Suddenly, an idea comes to him. He visualizes two number lines, intersecting at a 90° angle. He realizes that he can graph the fly's location on a piece of paper. Descartes called the main horizontal line the x-axis and the main vertical line the y-axis. He named the point where they intersect the origin.
3Descartes represented the fly's location as an ordered pair of numbers. The first number, the x-value, is the horizontal distance along the x-axis, measured from the origin.The second number, the y-value, is the vertical distance along the y-axis, also measured from the origin.
4Y-COORDINATEThe locations in the plane where the x and y values intersect are called coordinates.ORIGINX-COORDINATEIn the image on the right, three points — (0, 0), (-2, 5), and (3, -6.5) — are represented as graphed coordinates.
5The plane containing these points is called the Cartesian plane (in honor of Descartes), or the coordinate plane.Together, the x-axis, the y-axis, the coordinate plane, and all the coordinates make up the Cartesian coordinate system.CARTESIANCOORDINATESYSTEM
6The plane determined by a horizontal number line, called the x-axis, and a vertical number line, called the y-axis, intersecting at a point called the origin. Each point in the coordinate plane can be specified by an ordered pair of numbers.COORDINATE PLANEThe point (0, 0) on a coordinate plane, where the x-axis and the y-axis intersect.ORIGIN
8Points in Quadrant 2 have negative x but positive y coordinates. Points in Quadrant 1 have positive x and positive y coordinates.To make it easy to talk about where on the coordinate plane a point is, we divide the coordinate plane into four sections called quadrants.Points in Quadrant 3 have negative x and negative y coordinates.Points in Quadrant 4 have positive x but negative y coordinates.
10Write the coordinates of each point. B: (5, -3)C: (-1, -5)
11WRITE THE COORDINATES FOR EACH POINT B: (4, 6)C: (2, 1)D: (-4, 3)E: (-5, 0)F: (-3, -2)G: (0, -4)H: (4, -4)
12EVERY POINT THAT FITS ON A LINE IS CALLED “COLLINEAR”. Every straight line can be represented by an equation: y = mx + b. The coordinates of every point on the line will solve the equation if you substitute them in the equation for x and y.EVERY POINT THAT FITS ON A LINE IS CALLED “COLLINEAR”.THESE POINTS ARE “COLLINEAR”.y = 2x + 10 = 2(1) + 1== YES3 = 2(1) + 1== YES5 = 2(2) + 1== YES
13All segments shown are parallel to either the x- or y-axis All segments shown are parallel to either the x- or y-axis. Determine the ordered pair that represents each point.J: ( , )– 612G: ( , )– 6B: ( , )1N: ( , )12F: ( , )81E: ( , )8– 2
14Determine whether the following points are “collinear” to “G” and “H”. POINTS G(1, – 1) AND H(3, 3) LIE ON THE LINE “y = 2x – 3”.Determine whether the following points are “collinear” to “G” and “H”.I (0, – 3)y = 2x – 3 – 3 = 2(0) – 3YESJ (2, 1) 1 = 2(2) – 3YESK (– 3, –8) –8 = 2(–3) – 3NOL ( 5, 7) 7 = 2(5) – 3YES 16 = 2(10) – 3NOM ( 10, 16)