The line segment joining the points A(3, 2) and B(5, 1) is divided at the point P in the ratio 1:2 and it lies on the line 3x - 18y + k = 0. Find the value of k.

Given that, the line segment joining the points A (3, 2) and B (5, 1) is divided at the point p in the ratio 1:2

By using the section formula for internal ratio;

∴ Coordinates of point P =

As given in the question;

The point P lies on the line 3x – 18y + 5 = 0

∴

→11 - 30 + k = 0

k = 19 = 0

k = 19

Hence, the value of k is 19