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The straight line 2x + y = k goes through the point that divides the segment joining (1,1) and (2,4) internally in the ratio 3:2. What is the value of k?

1. 29/5
2. 5
3. 6
4. 11/5

Correct answer: 6

Solution

To find the value of k, we first determine the coordinates of the point that divides the segment joining (1,1) and (2,4) in the ratio 3:2 using the section formula. This gives us the point (1.6, 2.6). Substituting these coordinates into the equation of the line 2x + y = k, we find that k equals 6.

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