Question

Find the ratio in which the line 2x + 3y – 5 = 0 divides the line segment which joining the points (8, -9) and (2, 1). Find the coordinate of dividing point.

Answer 1

Let given line divides the line segment joining the points A(8, -9) arid B(2, 1) in the ratio λ : 1.

Let co-ordinate of point P

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

So, 2((2λ + 8)/(λ + 1)) + 3((λ - 9)/(λ + 1)) = 0

⇒ 2(2λ + 8) +3(λ – 9) -5(λ + 1) = 0

⇒ 4λ + 16 + 3λ – 27 – 5λ – 5 = 0

⇒ 2λ – 16 = 0

⇒ λ = 16/2

⇒ λ : 1 = 8 : 1

Hence required ratio

from equations (i), coordinate of point P.

= (24/9, -1/9)

= (8/3, -1/9)

Hence required ratio = 8 : 1 and co-ordinate of point = (8/3, - 1/9)