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In triangle ABC, the vertices are A = (alpha, beta), B = (1, 2), and C = (2, 3), where alpha and beta are integers and A lies on the line y = 2x + 3. If the area of triangle ABC belongs to the interval [2, 3), how many distinct sets of coordinates for A are possible?
- 1
- 2
- 3
- 4
Correct answer: 2
Solution
B and C are fixed, so BC is a fixed segment. B=(1,2), C=(2,3): line BC has equation y = x + 1. Area = (1/2)*|BC|*d(A, BC). Since A must be an integer point on y = 2x+3, find which integers give area in [2, 3).
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