6.6 Graphing Linear Equations 339 We indicate the location of a point in the rectangular coordinate system by means of an ordered pair of the form x y ( , ). The x-coordinate is always placed first, and the y-coordinate is always placed second in the ordered pair. Consider the point illustrated in Fig. 6.4. Since the x-coordinate of the point is 5 and the y-coordinate is 3, the ordered pair that represents this point is (5, 3). 24 25 2221 23 24 1 2 3 4 5 4 5 3 2 1 25 22 23 21 y 2nd quadrant 1st quadrant 3rd quadrant 4th quadrant Origin (0, 0) x Figure 6.3 y 24 25 2221 23 24 1 2 3 4 5 4 5 3 2 1 25 22 23 21 x (5, 3) Figure 6.4 Did You Know? Hollywood’s Four Quadrants m A scene from Indiana Jones and the Dial of Destiny. In the movie industry, a fourquadrant movie is one which appeals to all four major demographic groups or quadrants of the moviegoing audience: both male and female, and both over- and under-25 years old. The quadrants are: (1) male under 25, (2) female under 25, (3) male 25 and older, and (4) female 25 and older. If a studio produces a movie that appeals to all four quadrants , it is likely to have a hit movie. If the movie appeals to none of the four quadrants, the movie is likely to fail. Many four-quadrant movies have sequels due to the expectation of making large profits for the studios. Some examples of four-quadrant movies are: Star Wars, Raiders of the Lost Arc, Toy Story, Lord of the Rings, Pirates of the Caribbean, Avatar, and Top Gun . The origin is represented by the ordered pair (0, 0). Every point on the plane can be represented by one and only one ordered pair x y ( , ), and every ordered pair x y (, ) represents one and only one point on the plane. Example 1 Plotting Points Plot the points A B C D ( 2, 4), (3, 2), ( 1, 3), (6, 0), − − − − and E(0, 4). − Solution Point A has an x-coordinate of 2− and a y-coordinate of 4. Project a vertical line up from 2− on the x-axis and a horizontal line to the left from 4 on the y-axis. The two lines intersect at the point denoted A (Fig. 6.5). The other points are plotted in a similar manner. 24 y 2221 23 1 2 3 4 5 6 7 5 3 2 1 25 22 23 21 x A(22, 4) B(3, 22) E(0, 24) C(21, 23) D(6, 0) 4 Figure 6.5 7 Now try Exercise 11 Example 2 A Parallelogram The points, A B, , and C are three vertices of a parallelogram with two sides parallel to the x-axis. Plot the three ordered pairs below and determine the coordinates of the fourth vertex, D, of the parallelogram. A B C (1, 2) (2, 4) (7, 4) FlixPix/Alamy Stock Photo
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