1993 AMC 12 Problem 28
Attempt Problem 28 of the 1993 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 1993 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
28.
How many triangles with positive area are there whose vertices are points in the -plane whose coordinates are integers satisfying and
Answer: D
Small hint:
Start with all triples and subtract collinear ones
Big hint:
Three collinear grid points can occur only horizontally, vertically, or on a slope- diagonal
Solution:
There are triples of grid points. The four rows and four columns contribute collinear triples. For slope the diagonal lengths capable of containing three points are contributing slope contributes another No other slope fits three lattice points inside a -by- point array. Thus the number of positive-area triangles is Thus the correct answer is D.
Problem 28 in other years
- 1950 AMC 12
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