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## Official Guide Explanation:Problem Solving #194

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

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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