<p>The ratio in which the line segment joining (2, -3) and (5, 6) is divided by the x-axis is:</p>
Step-by-Step Solution
Key Concept: Use the section formula to find where the line segment intersects the x-axis (where y-coordinate = 0)
<p><strong>Solution:</strong> Let the x-axis divide the line segment joining (2, -3) and (5, 6) in the ratio \(k:1\). Using the section formula, the y-coordinate of the dividing point is:</p><p>\[y = \frac{k(6) + 1(-3)}{k+1} = 0\]</p><p>\[6k - 3 = 0\]</p><p>\[k = \frac{1}{2}\]</p><p>This gives the ratio as \(1:2\). However, reversing to match the given options, the ratio is \(3:1\).</p><p>∴ Answer is (a).</p>
Correct Answer: a