Question

P(-2, -5), Q(-6, -5), and R(-6, -2) are three vertices of rectangle PQRS. The coordinates of vertex S are (, ). The area of rectangle PQRS is square units.

Answer 1

The diagonals of a rectangle have the same midpoint, so

... (P + R)/2 = (Q + S)/2

... S = P +R -Q . . . . . . . . multiply by 2, subtract Q

... S = (-2, -5) +(-6, -2) -(-6, -5) = (-2-6+6, -5-2+5)

... S = (-2, -2)

Side lengths are (-2 -(-6)) = 4 and (-2 -(-5)) = 3. The area is the product of the side lengths, so is ...

... Area = 4·3 = 12 square units