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A quadrilateral has vertices, taken in order, at A(−2, −1), B(1, 0), C(4, 3) and D(1, 2). Which description of this quadrilateral is correct?

Competition practiceGeometry
  • AA rectangle
  • BA rhombus
  • CA parallelogram that is neither a rectangle nor a rhombus
  • DA square

Step-by-Step Solution

AB = √ √10 and DC = √ √10; BC = √ √18 and AD = √ √18. Opposite sides are equal, and the vector from A to B equals the vector from D to C, so it is a parallelogram. It is not a rhombus because √10 ≠ √18, and it is not a rectangle because the diagonals AC = √52 and BD = 2 are unequal.
Answer: C) A parallelogram that is neither a rectangle nor a rhombus

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