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 (1) `(29)/5` (2) 5 (3) 6 (4) `(11)/5`

Options

A. `(29)/(5)`
B. 5
C. 6
D. `(11)/(5)`

Explanation

To solve the problem, we need to find the value of \( k \) such that the line \( 2x + y = k \) passes through the point that divides the line segment joining the points \( (1, 1) \) and \( (2, 4) \) in the ratio \( 3:2 \).

### Step 1: Find the coordinates of the dividing point
We can use the section formula to find the coordinates of the point that divides the line segment joining points \( (x_1, y_1) = (1, 1) \) and \( (x_2, y_2) = (2, 4) \) in the ratio \( m:n = 3:2 \).

The section formula states that the coordinates of the point dividing the segment in the ratio \( m:n \) are given by:

\[
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