Question

The mid points of the sides 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

Answer: (A)

Let the coordinates of A, B, C are
$(x_1,y_1),$
$(x_2{y}_2),(x_3{y}_3)$
respectively. Given mid points $D(6,1),E(3,5)$
and $F(-1,-2)$ of the sides AB, BC and CA of the triangle.
$\therefore$ $\frac{x_1+x_2}{2}=6,$
$\frac{y_1+y_2}{2}=1$
$\Rightarrow$ $\begin{array}{c}{x}_1+x_2=12,\\ y_1+y_2=2\end{array}\}$ ..(i)
Similarly, $\begin{array}{c}{x}_2+x_3=6,\\ y_2+y_3=10\end{array}\}$ ..(ii)
and $\begin{array}{c}{x}_1+x_3=-2\\ y_1+y_3=-4\end{array}\}$ ..(iii)
On solving Eqs. (i), (ii) and (iii), we get
$x_1=2,x_2=10,x_3=-4$ and $y_1=-6,y_2=8,y_3=2$
Now, the vertex opposite to D is C ie, $(-4,2)$