Chapter 2 Section 2 The Coordinate Plane

Coordinate System The point at which the number lines intersect is called the origin. The vertical number line is called the y-axis. The plane that contains the x- and y-axis is called the coordinate plane. The horizontal number line is called the x-axis.

Ordered Pair In mathematics an ordered pair of numbers is used to locate any point on a coordinate plane.

The first number in an ordered pair is called the x-coordinate The first number in an ordered pair is called the x-coordinate. It corresponds to a number on the x-axis. The second number is called the y-coordinate. It corresponds to a number on the y-axis. (1, 5) y-coordinate x-coordinate

Y 7 6 (1, 5) 5 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 X -1 -2 -3 -4 -5 -6 -7

The next coordinate x is 4 and y is -1. (4, -1) Example 1 This is the origin. (0, 0) Write an ordered pair that names each point. Start with the origin. Move left on the x-axis to find the x-coordinate of the first point . The x-coordinate is -2. (-2, 4) Move up along the grid lines to find the y-coordinate. The y-coordinate is 4. The next coordinate x is 4 and y is -1. (4, -1)

Your Turn Write an ordered pair that names each point. (3, 2) A (-4, 0) D C B (3, -3) (-1, -3)

A point can be named by both a letter and its ordered pair A point can be named by both a letter and its ordered pair. For example, P (2, 3) means point P has an x-coordinate of 2 and a y-coordinate of 3. To graph an ordered pair on a coordinate plane, draw a dot at the point that corresponds to the ordered pair. This is called plotting the point.

Example 2 Graph P(2, 3) on a coordinate plane. Start at the origin, (0, 0). The x-coordinate is 2. So, move 2 units to the right. The y-coordinate is 3. So, move 3 units up and draw a dot. Label the dot with the letter P.

Example 3 Graph Q (-3, 0) on a coordinate plane. Start at the origin, (0, 0). The x-coordinate is -3. So, move 3 units to the left. The y-coordinate is 0. So, the dot is placed on the axis.

Your Turn Graph each point on the coordinate plane. R (2, -4) S (-1, 4) T (0, -3) S T R

The x-axis and y-axis separate the coordinate plane into four regions, called quadrants. The quadrants are numbered as shown at the below. Note that the axes are not located in any of the quadrants. Quadrant I (+, +) Quadrant II (-, +) Quadrant III (-, -) Quadrant IV (+, -)

Example 4 Name the quadrant in which each point is located. A (5, -4) The x-coordinate is positive, and the y-coordinate is negative. So, point A is located in Quadrant IV.

Example 5 Name the quadrant in which each point is located. B (2, 0) Point B lies on the x-axis. It is not located in a quadrant.

Your Turn Name the quadrant in which each point is located. C (-2, 7) D(-4, 9) E (0, -3) C = Quadrant III D = Quadrant II E = none

You can use ordered pairs to show how data are related. Dolphins can swim at 30 mph over long distances. Then, 30x represents the total distance traveled. Evaluate the expression to find the distances traveled in 1, 2, and 3 hours. The graph the ordered pairs (time, distance). 100 90 80 70 60 50 40 30 20 10 Time (hours) Distance (miles) x 30x 1 30 2 60 3 90 Distance (mi) 2 3 4 Hours