1952 AMC 12 Problem 5

Attempt Problem 5 of the 1952 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1952 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

5.

The points (6,12)(6,12) and (0,−6)(0,-6) are connected by a straight line. Another point on this line is:
(3,3)(3,3)
(2,1)(2,1)
(7,16)(7,16)
(−1,−4)(-1,-4)
(−3,−8)(-3,-8)
Answer: A
Concepts:coordinate geometryslope
Small hint:
Find the slope through the two given points
Big hint:
The line has equation y=3x−6y=3x-6
Solution:
The slope is 12−(−6)6−0=3, \frac{12-(-6)}{6-0}=3, so the line is y=3x−6.y=3x-6. Substituting x=3x=3 gives y=3.y=3.
Thus, the correct answer is A.
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