1952 AMC 12 Problem 31
Attempt Problem 31 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.
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31.
Given points in a plane no three of which are collinear, the number of lines they determine is:
None of these
Answer: D
Small hint:
Each line is determined by choosing two of the points
Big hint:
The condition that no three are collinear ensures that different pairs determine different lines
Solution:
Every pair of points determines one line, and no line is counted by more than one pair because no three points are collinear. Therefore the number of lines is
Thus, the correct answer is D.