Question

A ray of light is sent along the line x-2y-3=0 upon reaching the line 3x-2y-5=0 the ray is reflected from it, find the equation of the line containing the reflected ray.

Answer 1

Find the intersection point:

x - 2y - 3 = 0    -------------- [ 1 ]

3x - 2y - 5 = 0  -------------- [ 2 ]

Find the value of x:

[ 2 ] - [ 1 ]:

2x - 2 = 0

2x = 2

x = 1

Find the value of y:

From [ 1 }:

(1) - 2y - 3 = 0

2y = -2

y = -1

The intersection point is (1, -1)

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Find the equation of the reflected ray:

The reflected ray is the perpendicular to x - 2y - 3 = 0

⇒ The gradient is the negative reciprocal of x - 2y - 3 = 0

Find the gradient:

x - 2y - 3 = 0

2y = x - 3

y = 1/2 x - 3/2

⇒ The gradient is 1/2

⇒ The gradient of the perpendicular line is - 2

Find the y-intercept:

y = mx + c

y = -2x + c

at point (1, -1)

-1 = -2(1) + c

-1 = 2 + c

c = -3

Equation :

y = -2x - 3

y + 2x + 3 = 0

Answer: Equation of the reflected ray is y + 2x + 3 = 0