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 m is perpendicular to segment PQ at point R, and PR = RQ, how many points on line m are equidistant from point P and point Q ?

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:

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

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

If you are preparing for the SAT, ACT, or an SAT math subject test, you may want to take a look at the Get 800 collection of test prep books.

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