Question

Prove that the points P (0, -4), Q (6, 2), R (3, 5) and S (-3, -1) are the vertices of a rectangle PQRS.

Answer 1

PQ = `sqrt((6 - 0)^2 + (2 + 4)^2) = 6sqrt(2)"units"`

QR = `sqrt((6 -3)^2 + (2 - 5)^2) = 3sqrt(2)"units"`

RS = `sqrt((3 +3)^2 + (5 + 1)^2) = 6sqrt(2)"units"`

PS = `sqrt((-3 - 0)^2 + (-1 + 4)^2) = 3sqrt(2)"units"`

PR = `sqrt((3 - 0)^2 + (5 + 4)^2) = 3sqrt(10)"units"`

QS = `sqrt((6 +3)^2 + (2 + 1)^2) = 3sqrt(10)"units"`

∵ PQ = RS and QR = PS,
Also PR = QS
∴ PQRS is a rectangle.