Question

A ray of light passing through the point $A(1,2)$ is reflected at a point $B$ on the x-axis line mirror and then passes through $(5,3)$. Then the equation of $AB$ is -

• A. $5x+4y=13$
• B. $5x-4y=-3$
• C. $4x+5y=14$
• D. $4x-5y=-6$

Answer 1

The correct option is A $5x+4y=13$

The ray passes through $A(1,2)$ and reflects at $B$ and passes through $(5,3)$

The image of $(5,3)$ with respect to $x-axis$ is $(5,-3)$

The line $AB$ passes through the image of $(5,3)$

The slope of line is $\frac{2+3}{1-5}=\frac{-5}{4}$

So the equation of line is $y-2=\frac{-5}{4}(x-1)$

$4y-8=-5x+5$

$⟹5x+4y-13=0$