<p>If a line intercepted between the coordinate axes is trisected at a point \(A(4, 3)\), which is nearer to <em>x</em>-axis, then its equation is</p>
Step-by-Step Solution
Key Concept: If point A(4,3) trisects a line segment between axes such that A is closer to the x-axis, then A divides the segment in ratio 1:2 from x-axis to y-axis. Use section formula with intercepts to find the line equation.
<p><strong>Step 1:</strong> Let the line intercept the x-axis at B(a, 0) and y-axis at C(0, b).</p><p><strong>Step 2:</strong> Since A(4, 3) is nearer to the x-axis and trisects BC, point A divides BC in ratio 1:2 (from B to C).</p><p><strong>Step 3:</strong> Using section formula: A divides BC in ratio 1:2, so<br>4 = (1·0 + 2·a)/(1+2) = 2a/3 ⟹ a = 6<br>3 = (1·b + 2·0)/(1+2) = b/3 ⟹ b = 9</p><p><strong>Step 4:</strong> The line passes through (6, 0) and (0, 9).</p><p><strong>Step 5:</strong> Using intercept form: x/6 + y/9 = 1<br>Multiply by 18: 3x + 2y = 18</p><p>∴ <strong>Answer: 3x + 2y = 18</strong></p>
Correct Answer: C