Official Guide Explanation:
Problem Solving #194




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Solution and Metadata

Question: 194
Page: 180
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Coordinate Geometry > Other
Category 2: Geometry > Intersecting Lines and Angles >
Category 3: Geometry > Perpendicular Lines >

Explanation: The slope of a line is the negative reciprocal of the slope of its perpendicular bisector. So, since the slope of y = x is 1, the slope of segment AB is -1. In other words, if you move over one unit to the right, you must also move down one unit. So, if A is (2,3) and we can assume that AB intersects the line shown at about x = 2.5, then B must be (3,2). If the x - axis is the perpendicular bisector of BC, BC must be a vertical line. Point B is two units above the x - axis, so point C must be two units below the x - axis, with the same x - coordinate. Thus, the coordinates of point C must be (3, - 2), choice (D).

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