Determine the ratio in which the line divides the line segment joining the points A (2, – 2) and B (3, 7)

Let the given line divide the line segment joining the points A(2, - 2) and B(3, 7) in a ratio k : 1

Coordinates of the point of division = ()

This point also lies on 2x + y - 4 = 0

Therefore,

2 () + () – 4 = 0

= 0

9k – 2 = 0

k =

Hence, the ratio in which the line 2x + y - 4 = 0 divides the line segment joining the points A(2, - 2) and B(3, 7) is 2:9