Let A (2, 3), B (1, 4), C (0, -2) and D (x, y) are vertices of a parallelogram ABCD. 1. Write the position vectors A, B, C and D.

Question

Let A (2, 3), B (1, 4), C (0, -2) and D (x, y) are vertices of a parallelogram ABCD.

1. Write the position vectors A, B, C and D. 
2. Find the value of x and y.

Answer 1

1. position vector of A = 2i + 3j

Position vector of B = i + 4j

Position vector of C = 0i - 2j

Position vector of D = xi + yj.

2. Since ABCD is a parallelogram, then

(1) ⇒ -i + j = -xi – (y + 2 )j

x = 1, -2 – y = 1 ⇒ y = -3

∴ D is (1, -3).