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Solution

Let $A = (x,0)$. Slope of incident ray $= \dfrac{2 - 0}{1 - x} = \dfrac{2}{1 - x}$ Slope of reflected ray $= \dfrac{3 - 0}{5 - x} = \dfrac{3}{5 - x}$ For reflection from $X$–axis: angle of incidence = angle of reflection. Hence, their slopes are negatives of each other: $\dfrac{2}{1 - x} = -\dfrac{3}{5 - x}$ $\Rightarrow 2(5 - x) = -3(1 - x)$ $\Rightarrow 10 - 2x = -3 + 3x$ $\Rightarrow 5x = 13 \Rightarrow x = \dfrac{13}{5}$ Thus, $A\left(\dfrac{13}{5}, 0\right)$.