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A quadrilateral has vertices, taken in order, at P(3, 0), Q(4, 5), R(−1, 4) and S(−2, −1). Which description of this quadrilateral is correct?

Competition practiceGeometry
  • AA rectangle that is not a square
  • BA square
  • CA rhombus that is not a square
  • DA trapezium with exactly one pair of parallel sides

Step-by-Step Solution

All four sides come out equal: PQ = √(1 + 25) = √26, QR = √(25 + 1) = √26, RS = √(1 + 25) = √26 and SP = √(25 + 1) = √26. Four equal sides make it a rhombus. It is not a square because the diagonals are unequal: PR = √(16 + 16) = √32 while QS = √(36 + 36) = √72.
Answer: C) A rhombus that is not a square

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