Question

The mid-points of the sides $BC,CA$ and $AB$ of $△ABC$ are $D(2,1),E(-1,-3)$ and $P(4,0)$ respectively. Find the co-ordinates of $A,B$ and $C$.

Answer 1

Let $A\equiv (x_1,y_1)$ ; $B\equiv (x_2,y_2)$ ; $C\equiv (x_3,y_3)$

So, $\frac{x_1+x_2}{2}=4$ and $\frac{y_1+y_2}{2}=0$

$\frac{x_2+x_3}{2}=2$ and $\frac{y_2+y_3}{2}=1$

$\frac{x_3+x_1}{2}=-1$ and $\frac{y_1+y_3}{2}=-3$

On solving equations in $x_1,x_2,x_3$ and $y_1,y_2,y_3$, we get $x_1=1$, $x_2=7$, $x_3=-3$ and $y_1=-4$, $y_2=4$, $y_3=-2$

So, $A\equiv (1,-4)$ ; $B\equiv (7,4)$ ; $C\equiv (-3,-2)$