Question:

<p><strong>Solution:</strong> By the law of reflection, the angle of incidence equals the angle of reflection. The reflection point <span class="math inline">\(B\)</span> on the x-axis can be found by reflecting one of the points across the x-axis. Reflect <span class="math inline">\(A(1, 2)\)</span> to get <span class="math inline">\(A'(1, -2)\)</span>. The reflected ray passes through the point <span class="math inline">\((5, 3)\)</span>, so the incident ray path lies on the line through <span class="math inline">\(A(1, 2)\)</span> and <span class="math inline">\(B\)</span>, which must also align with the reflection principle. Alternatively, reflect <span class="math inline">\((5,3)\)</span> to <span class="math inline">\((5, -3)\)</span>. The line through <span class="math inline">\(A(1, 2)\)</span> and <span class="math inline">\((5, -3)\)</span> gives the incident ray direction. Slope <span class="math inline">\(= \frac{-3-2}{5-1} = \frac{-5}{4}\)</span>. Equation: <span class="math inline">\(y - 2 = -\frac{5}{4}(x - 1)\)</span>, so <span class="math inline">\(4y - 8 = -5x + 5\)</span>, giving <span class="math inline">\(5x + 4y = 13\)</span>.</p>