Question

find the coordinates of the point of trisection of the line segment joining the points A (1,-2) and B (-3,-4)​

Answer 1

Given line segment joining the points A(1,-2)and B(-3,4)

Let P and Q be the points of trisection of AB i.e., AP = PQ = QB

Therefore, P divides AB internally in the ratio 1 : 2.

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

m x 2 + n x 1 m + n , m y 2 + n y 1 m + n   .  

= [{1(-3) + 2(1)} / (1 + 2), {1(4) + 2(-2)} / (1 + 2)], = (–1 / 3, 0)

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

= [{2(-3) + 1(1)} / (1 + 2), {2(4) + 1(-2)} / (1 + 2)], = (–5/3, 4/3)

Therefore, the coordinates of the points of trisection of the line segment joining A and B are (–1 / 3, 0) and (–5/3, 4/3).