<p>If the line \(2x + y = k\) passes through the point which divides the line segment joining the points \((1, 1)\) and \((2, 4)\) in the ratio \(3 : 2\), then \(k\) equals</p>
Step-by-Step Solution
Key Concept: Find the point that divides the line segment in ratio 3:2 using the section formula, then substitute into the line equation to find k.
<p><strong>Step 1:</strong> Apply the section formula. When point P divides the line segment joining A(1,1) and B(2,4) in ratio 3:2, the coordinates are:</p><p>P = ((3·2 + 2·1)/(3+2), (3·4 + 2·1)/(3+2))</p><p>P = ((6+2)/5, (12+2)/5) = (8/5, 14/5)</p><p><strong>Step 2:</strong> Since this point lies on the line 2x + y = k, substitute x = 8/5 and y = 14/5:</p><p>k = 2(8/5) + 14/5 = 16/5 + 14/5 = 30/5 = 6</p><p>∴ Answer: k = 6</p>
Correct Answer: C