<p>The area of triangle ABC is 20 cm². The coordinates of vertex A are (–5, 0) and B are (3, 0). The vertex C lies on the line <span class="math">x - y = 2</span>. The coordinates of C are:</p>
Step-by-Step Solution
Key Concept: Use the area formula with base AB on the x-axis and the constraint that C lies on the given line.
<p><strong>Step 1:</strong> The base AB lies on the x-axis with length = |3 - (-5)| = 8.</p><p><strong>Step 2:</strong> Area of triangle = ½ × base × height = 20, so height = 5.</p><p><strong>Step 3:</strong> Point C lies on line x - y = 2, so C = (c, c-2) for some c.</p><p><strong>Step 4:</strong> Distance from C to x-axis = |c - 2| = 5.</p><p><strong>Step 5:</strong> Either c - 2 = 5 or c - 2 = -5, giving c = 7 or c = -3.</p><p><strong>Step 6:</strong> When c = 7, C = (7, 5). When c = -3, C = (-3, -5).</p><p>∴ Answer is (b) (–3, –5) or (d) (7, 5), but (–3, –5) is among the given options.</p>
Correct Answer: B