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A light ray emerging from a point source at \(A(2,3)\) is reflected on the \(Y\)-axis at point ' \(B\) ' and passes through point \(C(5,10)\), then the coordinates of ' \(B\) ' are
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The correct answer is:
\((0,5)\)
Let point of reflection is \((0, y)\) then, by law of reflection,
Angle of incidence \(=\) Angle of reflection
\(\Rightarrow \tan \theta=\tan (-\theta)\) \{As angles are measured in opposite directions.\}
\(\begin{aligned}
& \Rightarrow \quad m_1=-m_2 \\
& \Rightarrow \quad \frac{y-3}{-2}=\frac{y-10}{5}
\end{aligned}\)
\(\begin{array}{rrr}
\Rightarrow & 5 y-15 & =-2 y+20 \\
\Rightarrow & 7 y & =35, y=5
\end{array}\)
So, point is \((0,5)\).
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