Question

Let the equations of the perpendicular bisectors of $AB$ and $AC$ in a traingle $ABC$ is $x+y=2$ and $2x-y=10$ respectively. If the coordinates of the point $A(0,10)$, then the equation of the line $BC$ is

• A. $y=2$
• B. $x+2y=20$
• C. $x+y=2$
• D. $x+y=6$

Answer 1

The correct option is A $y=2$

Let the coordinate of $B\equiv (x_1,y_1)$ and $C\equiv (x_2,y_2)$
As $x+y-2=0$ is perpendicular bisector of $AB,B$ is the image of $A$ about the line $x+y-2=0$
For $B$
$\Rightarrow \frac{x_1-0}{1}=\frac{y_1-10}{1}=-\frac{2(0+10-2)}{2}$
$\Rightarrow x_1=-8;y_1=2\therefore B\equiv (-8,2)$
For $C$
$\Rightarrow \frac{x_2-0}{2}=\frac{y_2-10}{-1}=-\frac{2(0-10-10)}{5}$
$\Rightarrow x_2=16;y_2=2\therefore C\equiv (16,2)$
$\Rightarrow BC:y=2$