Question

A ray of light is sent along the line which passes through the point $A(2,3)$. The ray is reflected from the point $P$ on $x$ axis. lf the reflected ray passes through the point $(6,4)$, then the cordinates of point $P$ are

• A. $\left(\frac{26}{7},0\right)$
• B. $(0,\frac{26}{7})$
• C. $(-\frac{26}{7},0)$
• D. $(0,0)$

Answer 1

The correct option is A $\left(\frac{26}{7},0\right)$

Let $B=(6,4)$

So, image of $A(2,3)$ about $x-$axis is $C(2,-3)$

So, equation of line passing through $B(6,4)$ & $C(2,-3)$ is

$y-4=\frac{7}{4}(x-6)$

$4y-7x=16-42$

$4y-7x=-26$ ...(1)

So, substitute $y=0,x=\frac{26}{7}$

$\therefore P=(\frac{26}{7},0)$