First slide

Equation of line in Straight lines

Question

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

Moderate

A

6
B

11/5
C

29/5
D

5

Solution

If P $(x, y)$ divides the line segment $A B$ in the ratio 3:2, then
$x = \frac{3 (2) + 2 (1)}{5}, y = \frac{3 (2) + 2 (1)}{5}$
$P (8 / 5, 14 / 5)$
As the line $2 x + y = k$ passes through $P$
$2 \times (8 / 5) + (14 / 5) = k \Rightarrow k = 6$

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