Find the coordinates of the points which divide the line segment joining the points (5, 7) and (8, 10) in 3 equal parts.

Let A = (5, 7) and B = (8, 10).

Let P and Q be the points of trisection of AB i.e., AP = PQ = QB.

∴ P divides AB internally in the ratio 1: 2.

We know that the coordinates of the point P(x, y) which divides the line segment joining the points A (x₁, y₁) and B (x₂, y₂) internally in the ratio m₁: m₂ are .

So, P(x, y) =

⇒ P(x, y) = (18/3, 24/3)

∴ P(x, y) = (6, 8)

Now, Q also divides AB internally in the ratio 2: 1.

So, Q(x, y) =

⇒ Q(x, y) = (21/3, 27/3)

∴ Q(x, y) = (7, 9)

Ans. The coordinates of points which divide the line segment joining the points A and B in 3 equal parts are P(6, 8) and Q(7, 9).