Determine the ratio in which 2x + 3y - 30 = 0 divides the line segment joiningA (3, 4) and B (7, 8) and the point at which it divides.

Let the P(a, b) be the 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 .
This point lies on the line 2x + 3y - 30 = 0.

⇒ 2(7k + 3) + 3(8k + 4) - 30(k + 1) = 0.
⇒ 14k + 6 + 24k + 12 - 30k - 30 = 0.
⇒ 8k - 12 = 0.
∴ The required ratio is 3: 2.
The coordinates of the point P is ( )