Problem 17 · 2011 Math Kangaroo
Hard
Geometry & Measurement
spatial-reasoning
You are given the three corner points of a triangle and want to add a fourth point to make the four corners of a parallelogram. In how many places can the fourth point be placed?
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Answer: C — 3
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Hint 1 of 2
Draw the triangle, then try sliding the new point off each of the three corners in turn.
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Hint 2 of 2
Each corner of the triangle can be the one that sits opposite the new point — count those choices.
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Approach: let each triangle corner be the one opposite the new point
- Draw the triangle with corners A, B, C; the fourth point joins them into a parallelogram.
- Pick which corner is opposite the new point: if it is A you get one parallelogram, if B another, if C a third.
- That gives three different spots for the fourth point, so the answer is 3.
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