Question

Find the points of trisection of the line segment joining the points:

(2, -2) and (-7, 4).

Answer 1

The co-ordinates of a point which divided two points `(x_1, y_1)` and `(x_2, y_2)` internally in the ratio m:n is given by the formula,

The points of trisection of a line are the points which divide the line into the ratio 1: 2

Here we are asked to find the points of trisection of the line segment joining the points A(2,-2) and B(-7,4).

So we need to find the points which divide the line joining these two points in the ratio1:2 and 2 : 1.

Let P(x, y) be the point which divides the line joining ‘AB’ in the ratio 1 : 2.

`(x,y) = (((1(-7) + 2(2))/(1 + 2))"," ((1(4) + 2(-2))/(1+2)))`

(x,y) = (-1,0)

Let Q(e, d) be the point which divides the line joining ‘AB’ in the ratio 2 : 1.

`(e, d) = (((1(2) + 2(7))/(1 + 2))"," ((1(-2) + 2(4))/(1 + 2)))`

(e, d)= (-4, 2)

Therefore the points of trisection of the line joining the given points are (-1, 0) and (-4, 2)