Show that the PQRS formed by P (2, 1), Q (-1, 3), R (-5, -3) and S (-2, -5) is a rectangle.

Question

Show that the \(\Box\)PQRS formed by P (2, 1), Q (-1, 3), R (-5, -3) and S (-2, -5) is a rectangle.

Answer 1

Proof:

By distance formula,

In \(\Box\)PQRS,

PQ = RS … [From (i) and (iii)  

QR = PS ...[Form (ii) and (iv)]

\(\Box\)PQRS is a parallelogram [A quadrilateral is a parallelogram if both the pairs of its opposite sides are congruent]

In parallelogram PQRS, PR = QS … [From (v) and (vi)] 

∴ \(\Box\)PQRS is a rectangle. [A parallelogram is a rectangle if its diagonals are equal]