Question

If P(2, –1), Q (3, 4), R (–2, 3) and S (–3, –2) are four points in a plane, show that PQRS is a rhombus but not a square. Also find its area.

Answer 1

Now, we can see that 

PQ = QR = RS = PS = √26 units, but 

PR ≠ QS 

⇒ PQRS is a quadrilateral whose all sides are equal, but diagonals are not equal. 

⇒ PQRS is a rhombus, not a square.

∴ Area of rhombus PQRS = \(\frac12\times\) (Product of diagonals)

= \(\frac12\times\) PR × QS

= \(\frac12\times\) 4√2 x 6√2 = 24 sq. units.