Question

A ray of light passing through in point (1, 2) reflate on the x-axis at point A and line reflected ray passed through the point (5, 3) co-ordinates of A= ___

• A. $(\frac{13}{5},0)$
• B. $(-\frac{13}{5},0)$
• C. $(0,\frac{13}{5})$
• D. none of these

Answer 1

The correct option is A $(\frac{13}{5},0)$

As per the question The ray reflected at x-axis

Let the cordinates of points A be (h,0).

and Suppose the point B(5,3) and C(1,2)

Let the angle between line $AC$ and x-axis be $\theta$

then the angle between $AB$ and x-axis is $180-\theta$

slope of AC=$\frac{0-2}{h-1}$

$⟹tan\theta =\frac{-2}{h-1}-\left(1\right)$

Slope of AB$=\frac{-3}{h-5}$

$⟹tan(180-\theta )=\frac{-3}{h-5}⟹-tan\theta =\frac{-3}{h-5}⟹tan\theta =\frac{3}{h-5}-\left(2\right)$

Equating eqs.(1) and (2)

$\frac{-2}{h-1}=\frac{3}{h-5}⟹-2h+10=3h-3⟹5h=13⟹h=\frac{13}{5}$

Hence the cordinates of point A is $(\frac{13}{5},0)$