Section 3.1 The Coordinate System, Graphing Equations, and the Midpoint Formula 149 Procedure: Plotting an Ordered Pair (x, y) Step 1: From the origin, move left or right to the x-value given in the ordered pair. Step 2: From this x-value, move up or down to the y-value given in the ordered pair. Step 3: Plot a point at this location on the coordinate system. The two axes divide the plane into four regions called quadrants. Quadrants are labeled with Roman numerals I, II, III, and IV, beginning in the upper right quadrant and rotating counterclockwise. 2 2 4 4 –2 –4 –2 –4 x y t (– +) t (+ +) (+ –) t (– –) t (a 0) (0 b) Procedure: Identifying a Point’s Location on the Coordinate System Step 1: Convert the coordinates to decimal form, if necessary. Step 2: Identify the point’s location. a. If both x and y are positive, the point is in Quadrant I. b. If x is negative and y is positive, the point is in Quadrant II. c. If both x and y are negative, the point is in Quadrant III. d. If x is positive and y is negative, the point is located in Quadrant IV. e. If x = 0, the point is on the y-axis. f. If y = 0, the point is on the x-axis. Note: Points that lie on the axes do not lie in any of the quadrants. Objective 1 Examples Plot each ordered pair on a rectangular coordinate system and identify its location. 1a. (2, -3) 1b. (-3, 2) 1c. (0, -2) 1d. (4, 0) 1e. a1 2 , 9 2 b 1f. a-5, - 4 3 b Solutions See Figure 3.1. 1a. (2, -3); Move 2 units right from the origin and 3 units down; Quadrant IV 1b. (-3, 2); Move 3 units left from the origin and 2 units up; Quadrant II 1c. (0, -2); Move 0 units right or left from the origin and 2 units down; y-axis 1d. (4, 0); Move 4 units right from the origin and 0 units up or down; x-axis 1e. a1 2 , 9 2 b = (0.5, 4.5); Move 0.5 units right from the origin and 4.5 units up; Quadrant I 1f. a-5, - 4 3 b = (-5, -1.3); Move 5 units left from the origin and 1.3 units down; Quadrant III 2 2 4 f c 4 –2 –4 –2 –4 x y Figure 3.1
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