Question

Three vertices of a paralleiogram taken in order are (-1, - 6), (2, -5) and (7, 2). The fourth vertex is

• A. (1, 4)
• B. (4, 1)
• C. (1, 1)
• D. (4, 4)

Answer 1

The correct option is B

(4, 1)

Let $(-1,-6)B(2,-5)$ and $C(7,2)$ be the given vertex. Let $D(h,k)$ be the fourth vertex.

The midpoints of AC and BD are $(3,-2)$ and $(\frac{2+h}{2},\frac{-5+k}{2})$ respectively.

We know that the diagonals of a parallelogram bisect each other.

$\therefore 3=\frac{2+h}{2}$ and $-2=\frac{-5+k}{2}$

$\Rightarrow y=4$ and $k=1$