Question

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

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

Answer 1

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

The mid points of the sides of a triangle are $D(6,1)E(3,5)$ and $F(-1,-2)$.

then $D,E,F,$ vertex opposite to $D$ forms a parallelogram.

we know that in a parallelogram, diagonals bisect each other ..they have same midpoint ..

let $G(x,y)$ be the vertex opposite to $D$

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

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

$6+x=2$

$x=-4$

and also, $1+y=3$

$y=2$

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