Problem 8 · 2014 Math Kangaroo
Easy
Geometry & Measurement
symmetryspatial-reasoning
Tom draws a square on the coordinate plane. One diagonal sits on the x-axis, with endpoints \((-1,0)\) and \((5,0)\). Which of the following points is also a corner of the square?
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Answer: B — \((2,3)\)
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Hint 1 of 2
The two diagonals of a square cross at its centre and have equal length.
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Hint 2 of 2
Find the centre, then go the same distance perpendicular to the given diagonal.
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Approach: use the equal, perpendicular diagonals of a square
- The given diagonal runs from (−1,0) to (5,0); its centre is (2,0) and its half-length is 3.
- The other diagonal is vertical through (2,0) with the same half-length, giving corners (2,3) and (2,−3).
- The listed point is (2,3).
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