Question

The mid-points of the sides of a triangle are $D(6,1),E(3,5)$ and $F(-1,-2)$ then vertex opposite to D is

• A. $(-4,2)$
• B. $(-4,5)$
• C. $(2,2)$
• D. $(10,8)$

Answer 1

The correct option is A $(-4,2)$

Given that mid-points are, $D(6,1)E(3,5)F(-1,-2)$

Let vertex opposite to $D$ be $P(x,y)$

Now DEPF form a parallelogram and diagonals bisect each other in a parallelogram.

Midpoint of DP=Midpoint of EF

$(\frac{6+x}{2},\frac{1+y}{2})=(\frac{3-1}{2},\frac{5-2}{2})$

$\frac{6+x}{2}=1$

$\frac{1+y}{2}=\frac{3}{2}$

$x=2-6=-4$ $y=3-1=2$

So the vertex opposite to D is $P(-4,2)$

Hence option $\text{A}$ is correct answer