Find the coordinates of the point of trisection of the line segment joining (1,-2) and (-3,4).

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.

∴ the coordinates of P, by applying the section formula, are

…(i)

Here, m₁ = 1, m₂ = 2

(x₁, y₁) = (1, -2) and (x₂, y₂) = (-3, 4)

Putting the above values in the above formula, we get

Now, Q also divides AB internally in the ratio 2: 1. So, the coordinates of Q are

…(i)

Here, m₁ = 2, m₂ = 1

(x₁, y₁) = (1, -2) and (x₂, y₂) = (-3, 4)

Putting the above values in the above formula, we get

Therefore, the coordinates of the points of trisection of the line segment joining A and B are