Draw Your Own Figure
Question 2 with Solution

Last week, I went over a strategy for solving certain math problems on standardized tests by drawing a figure, and I gave you four problems to try on your own. You can see that post here: Math Strategy: Draw Your Own Figure

Today I would like to give a solution to the second of those four problems. You can see a solution for the first problem here: Draw Your Own Figure: Question 1.

Example: If line is perpendicular to segment PQ at point R, and PRRQ, how many points on line m are equidistant from point and point ?

A) One
B) Two
C) Three
D) More than three

Try to solve the problem yourself before checking the solution below.

Solution: Recall first that equidistant means at the same distance. So we’re looking for points on line m that are at the same distance from P as they are from Q. Let’s begin by drawing a picture:

equidistant 1

Notice that R is equidistant from P and Q, so there is at least one. Let’s draw some more.

equidistant 2


Since there are 5 shown in the above picture, the answer is choice D.

Note: Every point on line m is actually equidistant from P and Q. m is the perpendicular bisector of line segment PQ

The perpendicular bisector of a line segment is a line perpendicular to the segment that passes through the midpoint of the segment.


More Problems with Explanations

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