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

Let the line 2x + 3y – 5 = 0 divides the line segment AB in the ratio of λ:1 at point P.

∴ Coordinates of P =

∵ Internal Division

=

But P lies on 2x + 3y – 5 = 0

→ 2(2λ + 8) + 3(λ – 9) – 5(λ + 1) = 0

→ 4λ + 16 + 3λ - 27 - 5λ – 5 = 0

→ 2λ – 16 = 0

→ λ = 8

→ λ:1 = 8:1

So, the point P divides the line in the ratio 8:1

∴ Point of division P =

Hence, the required point of division is

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