QJEEM12Maea26: JEE Main 2012 Mathematics - Class 11 JEEM12Maea26 Solution: If the line 2 x + y = k passes through the point which divides…

Question

Verified Solution • 2025–26 Session moderate

If the line

2 x + 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 :

Accepted Answer

The point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2 is

$= (\frac{3 \times 2 + 2 \times 1}{3 + 2}, \frac{3 \times 4 + 2 \times 1}{3 + 2})$

$= (\frac{6 + 2}{5}, \frac{12 + 2}{5}) = (\frac{8}{5}, \frac{14}{5})$

Since the line 2x + y = k passes through this point,

$∴$ $2 \times \frac{8}{5} + \frac{14}{5} = k$ or $\frac{30}{5} = k$ or, k = 6

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