Question

A light beam eminating from the point $A(3,10)$ reflects from the straight line $2x+y-6=0$ and then passes through the point $B(4,3)$. The equation of the reflected beam is:

• A. $2x+y-13=0$
• B. $x+3y-13=0$
• C. $3x+y-15=0$
• D. $x-3y+5=0$

Answer 1

The correct option is A $2x+y-13=0$

Let the line

$2x+y-6=0$

$y=-2x+6$

Hence the slope $m_1=-2$

Slope of reflecting lie and incident line are equal because angle of incident is equal to angle of reflection.

Therefore slope of reflecting line also $-2$

Hence by slope-point formula of line.

$y-y_1=m_1(x-x_1)$

$y-3=-2(x-4)$

$y-3=-2x+8$

$2x+y-13=0$

Hence, the equation of reflected beam.

$2x+y-13=0$