210. The line joining the points (1, -2) and (-3, 4) is trisected. Find the co-ordinates of the points of trisection. 

Fig. 7.28A.
Let the given points be A(3, -1) and B(-6, 5).
Let P and Q be the points of trisection of AB.
Then,    AP = PQ = QB = 1
Thus ‘P’ divides AB in the ratio 1 : 2.
Here, we have x₁ = 1,    y₁ = -2
x₂ = -3,    y₂ = 4
and    m₁ = 1    m₂ = 2
∴ The co-ordinates of ‘P’ are given by



Case II.

Fig. 7.29.
Now ‘Q’ divides AB in the ratio 2 : 1.
Here, we have x₁ = 1,    y = -2
x₂ = -3,    y₂ = 4
and    m₁ = 2    m₂ = 1
∴ The co-ordinates of ‘Q’ are given by

Hence, the co-ordinates of the points of trisection are