Problem 9 · 2021 Math Kangaroo
Medium
Geometry & Measurement
area
What is the area of the triangle whose vertices are \((p,q)\), \((3p,q)\) and \((2p,3q)\), where \(p,q > 0\)?
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Answer: C — \(2pq\)
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Hint 1 of 2
Two of the vertices share the same y-coordinate — use that side as the base.
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Hint 2 of 2
The height is the vertical distance to the third vertex; apply ½·base·height.
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Approach: pick a horizontal base and read off the height
- The points (p,q) and (3p,q) lie on the same horizontal line, so the base has length 3p − p = 2p.
- The third vertex (2p,3q) is a vertical distance 3q − q = 2q above that line.
- Area = ½ · 2p · 2q = 2pq.
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