Problem 4 · 2016 Math Kangaroo
Medium
Geometry & Measurement
spatial-reasoning
Five points are given in a Cartesian coordinate system: P(−1, 3), Q(0, −4), R(−2, −1), S(1, 1), T(3, −2). Four of these five points are vertices of a square. Which point does not belong there?
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Answer: A — P
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Hint 1 of 2
A square has four equal sides meeting at right angles.
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Hint 2 of 2
Test which four of the five points have all sides equal and perpendicular.
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Approach: check the square
- Q(0,−4), R(−2,−1), S(1,1), T(3,−2) give four equal sides (each of squared length 13) with right angles.
- Those four form a square.
- The leftover point is P, so P does not belong.
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