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P(0, 0), Q(3, 4), R(0, 8) and S(-3, 4) are joined in order, and all four sides come to 5 units. What is the most precise name for PQRS?

Class 10Distance FormulaGeometry — Coordinates
  • AA square, since all four sides are equal
  • BA rectangle, since opposite sides are equal
  • CA rhombus, because the diagonals PR = 8 and QS = 6 are unequal
  • DOnly a parallelogram, because the sides are not all equal

Step-by-Step Solution

Each side is 5: , and likewise QR, RS and SP. The diagonals are PR = |8 - 0| = 8 and QS = || = 6. Four equal sides make it a rhombus; a square would also need equal diagonals, and 8 is not 6. So it is a rhombus that is not a square.
Answer: C) A rhombus, because the diagonals PR = 8 and QS = 6 are unequal

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