Question

If the image of the point $(2,1)$ with respect to a line mirror is $(5,2),$ find the equation of the mirror.

Answer 1

Here,

Let l be line mirror and B is image of A

Let m be slope of line l

So,

$m\left(slopeofAB\right)=-1$

$m\left(\frac{2-1}{5-2}\right)=-1$

$m\left(\frac{1}{3}\right)=-1$

$m=-3$

M is mid point of AB

$M=(\frac{2+5}{2},\frac{2+1}{2})$

$M=(\frac{7}{2},\frac{3}{2})$

Equation line l is,

$y-y_1=m(x-x_1)$

$y-\frac{3}{2}=(-3)(x-\frac{7}{2})$

$\frac{2y-3}{2}=-3x+\frac{21}{2}$

$2y-3=-6x+21$

$6x+2y=24$

$3x+y=12$