196 Chapter 3 Graphing Linear Equations in Two Variables Points graphed in a rectangular coordinate system are defined by two numbers as an ordered pair, (x, y).The first number (called the x-coordinate, or the abscissa) is the horizontal position from the origin.The second number (called the y-coordinate, or the ordinate) is the vertical position from the origin. Example 2 shows how points are plotted in a rectangular coordinate system. Plotting Points in a Rectangular Coordinate System Example 2 Plot the points. a. b. c. d. 14, 52 14, 52 11, 32 13, 12 1 2 7 3 b a 12, 02 10, 02 1p, 1.12 e. , f. g. h. Solution: See Figure 3-3. a. The ordered pair indicates that and 14, 52 x 4 . Beginning at the origin, move 4 units in y 5 the positive x-direction (4 units to the right), and from there move 5 units in the positive y-direction (5 units up).Then plot the point. The point is in Quadrant I. 14, 52 b. The ordered pair indicates that and . Move 4 units in the negative x-direction (4 units to the left), and from there move 5 units in the negative y-direction (5 units down).Then plot the point. The point is in Quadrant III. (1, 3) (2, 0) 3 1 11, 32 x 1 y 3 5 4 3 2 1 1 2 3 (0, 0) (, 1.1) c. The ordered pair indicates that and . Move 1 unit to the left and 3 units up.The point is in Quadrant II. 13, 12 x 3 y 1 d. The ordered pair indicates that and . Move 3 units to the right and 1 unit down.The point is in Quadrant IV. e. The improper fraction can be written as the mixed number . Therefore, to plot the point move to the right unit, and down units.The point is in Quadrant IV. 12, 02 y 0 f. The point indicates .Therefore, the point is on the x-axis. g. The point is at the origin. h. The irrational number, can be approximated as 3.14.Thus, the point is located approximately 3.14 units to the right and 1.1 units up.The point is in Quadrant I. Skill Practice 5. Plot the points. 5 2 A(3, 4) B(2, 2) C(4, 0) Da , E(5,2) 1 2 b 1p, 1.12 p, 10, 02 213 1 1 , 12 2 73 2 213 73 x 4 y 5 54 2 4 5 1 2 3 4 5 y x (4, 5) (4, 5) (3, 1) ( , ) 12 73 Figure 3-3 TIP: Notice that changing the order of the x- and y-coordinates changes the location of the point. For example, the point is in Quadrant II, whereas is in Quadrant IV (Figure 3-3). This is why points are represented by ordered pairs. The order of the coordinates is important. Avoiding Mistakes Points that lie on either of the axes do not lie in any quadrant. Answer 5. 5 4 3 2 1 5 43 21 1 2 3 4 5 1 2 3 4 5 A D B E y x C 13, 12 11, 32
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