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 the point $$A$$ are

A
(135,0)
B
(513,0)
C
(7,0)
D
None of these

Solution

## The correct option is B $$\left ( \displaystyle \frac{13}{5},0 \right )$$Let the coordinates of point A be $$(a,0)$$Let OL be the normal .$$\Rightarrow \angle BAL=\angle CAL =\phi$$Let $$\angle CAX=\theta$$$$\Rightarrow \angle OAB=\theta$$So, $$\angle BAX={90}^{0}+\phi$$Slope of line Ac $$=\displaystyle \tan ({ 90 }^{ 0 }-\phi )=\frac { 3 }{ 5-a }$$$$\Rightarrow \cot \phi =\dfrac { 3 }{ 5-a }$$                ......(i)Slope of line AB $$=\displaystyle \tan ({ 90 }^{ 0 }+\phi )=\frac { 2 }{ 1-a }$$$$\Rightarrow \cot \phi =\dfrac { 2 }{ a-1 }$$                ......(ii)From (i) and (ii),$$\Rightarrow \dfrac { 3 }{ 5-a } =\dfrac { 2 }{ a-1 }$$$$\Rightarrow a=\dfrac { 13 }{ 5 }$$Hence, the image is $$(\dfrac { 13 }{ 5 } ,0)$$Physics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More