Problem:
How many triangles with positive area are there whose vertices are points in the -plane whose coordinates are integers satisfying and
Answer Choices:
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B.
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E.
Solution:
There are sets of points. We must exclude from our count those sets of three points that are collinear. There are vertical and horizontal lines of four points each. These lines contain sets of collinear points. Similarly, there are sets of collinear points that determine lines of slope . Since there are no other sets of collinear points, the number of triangles is .
