5 1 The Coordinate Plane OBJECTIVES You need

5 -1: The Coordinate Plane OBJECTIVES: You need to be able to graph ordered pairs on a coordinate plane. What is a coordinate plane? Well, it looks like this We have the following terms related to the coordinate plane: • axes - the two perpendicular number lines which make up the coordinate plane one is the x-axis, the other is the y-axis • origin - the point at the center of the coordinate plane (0, 0) • x-axis - the horizontal number line • y-axis - the vertical number line • quadrants - the four regions created by the crossing of the two axes © William James Calhoun, 2001

5 -1: The Coordinate Plane We use coordinates to locate any point in the coordinate plane. A coordinate is a point in the plane given by an ordered pair: (x, y) The “x” tells you how far right/left the point is from the origin. The “y” tells you how far up/down the point is from the origin. The point (2, 4) would be 2 to the right and 4 up from the origin. The point (-3, 5) would be 3 to the left and 5 up from the origin. The point (4, -2) would be 4 to the right and 2 down from the origin. positive y values negative x values positive x values negative y values © William James Calhoun, 2001

5 -1: The Coordinate Plane Once you have the basics down, reading and plotting points on a coordinate plane becomes easy. It is critical that you remember: x is horizontal y is vertical x comes first in the ordered pair y comes second in the ordered pair (x, y) © William James Calhoun, 2001

5 -1: The Coordinate Plane EXAMPLE 1: Write ordered pairs for points E, F, G, and H shown below. Name the quadrant in which each point is located. Start with point E. right 4 How far right/left do you go from the origin to get to point E? down 2 How far up/down do you go from the origin to get to point E? right is positive for x down is negative for y so E = (4, -2) I will use a chart to finish the problem. To graph an ordered pair means to put a dot at the coordinate matching the ordered pair’s x- and y-values. The next slide shows how to do this. © William James Calhoun, 2001

5 -1: The Coordinate Plane EXAMPLE 2: Plot the following points on a coordinate plane. A. N(-3, -5) start at the origin x = -3 so move… 3 spaces left y = -5 so move… 5 spaces down draw a dot at that spot B B. K(-4. 5, 8) start at the origin x = -4. 5 so move… 4. 5 spaces left y = 8 so move… 8 spaces up draw a dot at that spot C. L(6, 0) start at the origin x = 6 so move… 6 spaces right y = 0 so move… 0 spaces down/up draw a dot at that spot C A © William James Calhoun, 2001

5 -1: The Coordinate Plane 5. 1. 1 COMPLETENESS PROPERTY FOR POINTS IN THE PLANE 1. Exactly one point in the plane is named by a given ordered pair of numbers. 2. Exactly one ordered pair of numbers names a given point in the plane. The next example uses graphing, but relates it to maps and travel. © William James Calhoun, 2001

5 -1: The Coordinate Plane EXAMPLE 3: Use ordered pairs to name all the sectors that Interstate Highway 35 passes through on the map of San Antonio, Texas, shown below. I-35 begins in the southwest corner and extends through San Antonio to the northeast corner. Part of it shares the same path as I 410. I-35 goes through (1, D), continuing through (2, D), across the southeast corner of (2, C), turning upward through (3, C), across the southern portion of (3, B), sharing the path with I-410 through (4, B), and exiting the map at the eastern edge of (4, A). © William James Calhoun, 2001