Question

Find the coordinates of a point of a trisection (point dividing in 3 equal parts )of a line segment joining the point A(1,-2andB(-3,-4).

Answer 1

A(1,-2)-----P(x,y)-------------B(-3,-4)

Let P(x,y) be one trisection point

as it is trisection point P divides AB in the ratio 1:2

apply section formula

(x,y) = [{(1×-3)+(2×1)}/(1+2),{(1×-4)+(2×-2)}/(1+2)]

(x,y) = [-1/3,-8/3]

Let another point Q(x1,y1) divide AB in the ratio 2:1

apply section formula

(x1,y1) = [{(2×-3)+(1×1)}/(2+1),{(2×-4)+(1×-2)}/(2+1)]

(x1,y1) = [-5/3,-10/3]