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The quadrilateral ABCD has vertices A(-1, -1), B(5, 1), C(4, 4) and D(-2, 2). Work out the four sides and the two diagonals, then name the figure as precisely as you can.

Class 10Distance FormulaGeometry — Coordinates
  • AA square
  • BA rectangle: the diagonals are equal but adjacent sides are not
  • CA rhombus, since all four sides are equal
  • DA parallelogram whose diagonals are unequal

Step-by-Step Solution

and , so opposite sides are equal and ABCD is a parallelogram. Both diagonals come to and ; a parallelogram with equal diagonals is a rectangle. Adjacent sides and differ, so it is not a square.
Answer: B) A rectangle: the diagonals are equal but adjacent sides are not

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