Question

The extremities of diagonal of parallelogram are the points

(3, – 4) and (– 6,5) if third vertex is (– 2,1), then fourth vertex is

• A. (1,0)
• B. (–1,0)
• C. (1,1)
• D. None of these

Answer 1

Answer: (B)

(–1,0)

Answer 2

Let $A(3, - 4)$ and $C( - 6,5)$ be the ends of diagonal of parallelogram ABCD. Let $B( - 2,1)$ and D be (x, y), then mid points of diagonal AC and BD coincide. So, $\frac{x - 2}{2} = \frac{- 6 + 3}{2}$ and $\frac{y + 1}{2} = \frac{5 - 4}{2}$

$x = - 1,y = 0$.

∴ Coordinates of D are (–1, 0)