Question

Determine the ratio in which the line 2x+3y=30 divides the line joining A(3,4) and B(7,8) and at what point

Answer 1

Let the P(a,b) be te point which divides the line segment joining A(3,4) and B(7,8) in the ratio k:1.

Then coordinates of the point P is (7k+3/k+1 , 8k+4/k+1).

This point lies on the line 2x + 3y - 30 = 0.

∴ 2(7k+3/k+1) +3 (8k+4/k+1) - 30 = 0.

∴ 2(7k+3) +3 (8k+4) - 30(k+1) = 0.

∴ 14k + 6 + 24k + 12 - 30k - 30 = 0.

∴ 8k - 12 = 0

∴ k = 3/2

∴ The required ratio is 3:2

The coordinates of the point P is (21+6/5 , 24+8/5) = (27/5 , 32/5)