# 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. If the equation of the line containing reflected ray is #ax-2y = b#, then find the value of#(a+b)#?

##### 1 Answer

#### Explanation:

We are given 3 equations:

Find the slope of the line corresponding to equation [1]

The angle that it forms with the x axis is

Find the slope of the line corresponding to equation [2]:

The angle that it forms with the x axis is

The angle from line [1] to line [2] is the angle of incidence:

Find the slope of the line corresponding to equation [3]:

The angle that it forms with the x axis is

The angle from line [2] to line [3] is the angle of reflection:

Because the angle of incidence equals the angle of reflection we can set the right side of equation [4] equal to the right side of equation 5:

Substitute into equation [3]:

Find the point of intersection of lines [1] and [2]:

Subtract [1] from [2]:

Substitute 1 for x into equation [1]:

#-2y -2 = 0

The point is

Equation [3.1] must contain the same point: