Question

If $(-2,6)$ is the image of the point $(4,2)$ with respect to the line $L=0$, then $L=$

• A. $6x-4y-7=0$
• B. $2x-3y-5=0$
• C. $3x-2y+5=0$
• D. $3x-2y+10=0$

Answer 1

The correct option is C $3x-2y+5=0$

Slope of line joining the image $Q(-2,6)$ and the point $P(4,2)$ is $-\frac{2}{3}$
So, the slope of mirror $L$ is $\frac{3}{2}$
Mid-point of $PQ$ is $(1,4)$
Since, the image and point are equidistant from mirror. So, this point $(1,4)$ lies on the mirror.
So, the equation of mirror is
$y-4=\frac{3}{2}(x-1)$
$\Rightarrow 3x-2y+5=0$