I need help...especially with part b...

Question

The figure at right shows a parallelogram PQRS, three of whose vertices are P = (0,0), Q = (a,b), and S = (c,d).

(a) Find the coordinates of R.

(b) Find the area of PQRS, and simplify your formula.

Answer 1

(a) Let R(x, y). Then PQ = <a, b> = SR = <x - c, y - d>; x - c = a; x = a + c; y - d = b; y = b + d; R(a + c, b + d)

(b) PR = <c, d>; [PQ, CR] = det [(i j k) (a b 0) (c d 0)] = (ad - bc)k;

Area PQRS = Iad - bcI