A light ray emerging from a point source at \(A(2,3)\) is reflected on the \(Y\)-axis at point ' \(B\) ' and…

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
  1. \((5,0)\)
  2. \((0,5)\)
  3. \((0,2)\)
  4. \((2,0)\)

Solution


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 \((0,5)\).

Asked in: AP EAMCET 2020 (17 Sep Shift 2)

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