If P (9a – 2, - b) divides line segment joining A (3a + 1, - 3) and B (8a, 5) in the ratio 3:1, then find the values of a and b.

Let P (9a – 2, - b) divides AB internally in the ratio 3:1.

By the section formula;

Internal section formula, the coordinates of point P divides the line segment joining the point (x₁, y₁), (x₂, y₂) in the ratio m₁:m₂ internally is

For 9a – 2, we have;

9a – 2 =

→ 36a – 8 = 27a + 1

And for – b we have;

- b =

Hence, the values of a and b are 1 and - 3.