Question

The points $(-1,0)$ and $(-2,1)$ are the two extremities of a diagonal of a parallelogram. If $(-6,5)$ is the third vertex, then the fourth vertex of the parallelogram is

• A. (2, -6)
• B. (2, -5)
• C. (3, -4)
• D. (-3, 4)
• E. (3, -5)

Answer 1

Answer: (C)

Let the points of parallelogram are $A(-2,1),B(-6,5)$, $C(-1,0)$ and $D(x,y)$

We know that, diagonals of parallelogram bisect each other.
$\left(\frac{-2-1}{2},\frac{1+0}{2}\right)=\left(\frac{x-6}{2},\frac{y+5}{2}\right)$
$\Rightarrow \frac{-3}{2}=\frac{x-6}{2}$ and $\frac{1}{2}=\frac{y+5}{2}$
$\Rightarrow -3=x-6$ and $1=y+5$
$\Rightarrow x=-3+6$ and $y=1-5$
$\Rightarrow x=3$ and $y=-4$
Thus, coordinates of fourth vertex of paralleogram are $(3,-4)$