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

Engineering

Mathematics

Section Formulae and Centres of a Triangle

Question

$\frac{29}{5}$

$\frac{11}{5}$

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Since, M divides A & B in the ratio 3 : 2.

$∴$ Coordinates of M are $(\frac{6 + 2}{5}, \frac{12 + 2}{5}) \equiv (\frac{8}{5}, \frac{14}{5})$

M lies on the line 2x + y = k

$∴$ $k = 2 \cdot \frac{8}{5} + \frac{14}{5} = 6$