SAT Math Multiple Choice Practice Question 34: Answer and Explanation

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Question: 34


In this figure, the slope of line PQ is -1/3, and M is the midpoint of the line PQ. What are the coordinates of point P?

A. (8, -1)
B. (9, -1)
C. (10, -2)
D. (11, -2)
E. (12, -2)

Correct Answer: D


D. A slope of -1/3 means that the line goes down 1 space every time it moves 3 spaces to the right. Because point M is on the x-axis, the line has gone down 2 spaces by the time it reaches M, so it must have moved 6 spaces to the right. In other words, point M is at (5, 0). Point M is the midpoint of the line, which means that it's halfway to point P. So to get to point P, you need to move another 2 spaces down and 6 spaces right, which puts you at (11, -2).

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