Question

A ray of light coming from the point (1 2) is reflected at a point a on the x axis and then passes through the point (5,3). the coordinates of a are

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A ray of light coming from the point (1,2) is reflected at a point A on the x-axis and then passes through the point (5,3). The coordinates of the point A are

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ANSWER

Let the coordinates of point A be (a,0)

Let OL be the normal .

⇒∠BAL=∠CAL=ϕ

Let ∠CAX=θ

⇒∠OAB=θ

So, ∠BAX=90

0

+ϕ

Slope of line Ac =tan(90

0

−ϕ)=

5−a

3

⇒cotϕ=

5−a

3

......(i)

Slope of line AB =tan(90

0

+ϕ)=

1−a

2

⇒cotϕ=

a−1

2

......(ii)

From (i) and (ii),

⇒

5−a

3

=

a−1

2

⇒a=

5

13

Hence, the image is (

5

13

,0)

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