Question

PQRS is a rectangle formed by joining the points P(-1, -1), Q(-1, 4) ,R(5, 4) and S(5, -1). A, B, C and D are the mid-points of PQ, QR, RS and SP respectively. Is the quadrilateral ABCD a square, a rectangle or a rhombus? Justify your answer.

Answer 1

A, B, C and D are mid points of PQ, QR, RS & SP respectively.

∴ AC is perpendicular to BD.

∴ ABCD can be a square or rhombus.

∴ AB and BC are not perpendicular

⇒ ABCD is rhombus as diagonals are perpendicular and sides are not perpendicular.