Question

Find the image of the point P$(-1,2)$ in the line mirror $2x-3y+4=0$

Answer 1

Let image of P is Q

$\therefore$ PM = MQ & PQ $\perp$ AB

Let Q is (h, k)

$\therefore$ M is $(\frac{h-1}{2},\frac{k+2}{2})$

It lies on 2x - 3y + 4 = 0

$\therefore 2\left(\frac{h-1}{2}\right)-3\left(\frac{k+2}{2}\right)+4=0$

or 2h - 3k = 0 .......(i)

slope of PQ = $\frac{k-2}{h+1}$

$PQ\perp AB$

$\therefore \frac{k-2}{h+1}\times \frac{2}{3}=-1$

$\Rightarrow$ 3h + 2k - 1 = 0 ........(ii)

solving (i) & (ii) we get h = $\frac{3}{13}$, k = $\frac{2}{13}$

$\therefore$ Image of P(-1, 2) is Q$(\frac{3}{13},\frac{2}{13})$