Question

Find the coordinates of the points of trisection of the line segment joining the points A(–1, 4) and B(–3, –2).

Answer 1

Let A(–1, 4) and B(–3, –2).

First point of trisection, P, divides AB in 1 : 2.

Using the section formula:

`x_p = (1 xx (-2) + 2 xx 4)/(1 + 2)`

= `(-2 + 8)/3`

= `6/3`

= 3

`y_P = (1 xx (-3) + 2 xx (-1))/(1 + 2)`

= `(-3 + (-2))/3`

= `(-5)/3`

So, `P(2, -5/3)`.

Second point of trisection, Q, dicides AB in 2 : 1:

`x_Q = (2 xx (-2) + 1 xx 4)/(2 + 1)`

= `(-4 + 4)/3`

= `0/3`

= 0

`y_Q = (2 xx (-3) + 1 xx (-1))/(2 + 1)`

= `(-6 + (-1))/3`

= `(-7)/3`

So, `Q(0, - 7/3)`.

The coordinates of the points of trisection are `(2, -5/3)` and `(0, - 7/3)`.