Stitz-Zeager_College_Algebra_e-book

# 2 we close with a more abstract application of the

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Unformatted text preview: es of the midpoint. 1.1 The Cartesian Coordinate Plane 9 Example 1.1.5. Find the midpoint of the line segment connecting P (−2, 3) and Q(1, −3). Solution. M x1 + x2 y1 + y2 , 2 2 (−2) + 1 3 + (−3) , 2 2 10 −, 22 1 − ,0 2 = = = = The midpoint is 1 − ,0 . 2 We close with a more abstract application of the Midpoint Formula. We will revisit the following example in Exercise 14 in Section 2.1. Example 1.1.6. If a = b, prove the line y = x is a bisector of the line segment connecting the points (a, b) and (b, a). Solution. Recall from geometry that a bisector is a line which equally divides a line segment. To prove y = x bisects the line segment connecting the (a, b) and (b, a), it suﬃces to show the midpoint of this line segment lies on the line y = x. Applying Equation 1.2 yields M = = a+b b+a , 2 2 a+b a+b , 2 2 Since the x and y coordinates of this point are the same, we ﬁnd that the midpoint lies on the line y = x, as required. 10 Relations and Functions 1.1.2 Exercises √ 1. Plot and label the points A(−3, −7), B (1.3, −2), C (π, 10), D(0, 8),...
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