Question

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

(i) (5, -6) and (- 7, 5),

(ii) (3, -2) and (- 3, - 4)

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

Answer 1

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

Therefore, P divides AB internally in the ratio of 1:2, thereby applying section formula, the coordinates of P will be

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

(ii) Let P, Q be the point of tri section of AB i.e.,

AP=PQ=QB

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

Hence by applying section formula, Coordinates of P are

Now, Q also divides as internally in the ratio of 2:1 

So, the coordinates of Q are

(iii) Let P and Q be the points of trisection of AB i.e., AP=PQ=OQ

Therefore, P divides AB internally in the ratio 1 : 2. Therefore, the coordinates of P, by applying the section formula, are

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