Question

point p(5,-3) is one of the two pints of trisection of the line segment joining the points a(7,-2) & b(-1,5) near to a. find the coordinates of the other point of trisection

Solution

A---------p----------Q------------B
let Q is the unknown point
because according to question
AP=PQ=QB
In the question it is not given that Q is the mid point of QB.then how con we presume it?

Answer 1

In the question it is given that P is on of the point of trisection of the line AB.
so to divide the line into 3 equal parts we want two points P and Q, so
AP=PQ=QB
Since it is three equal parts we can say that Q is the midpoint of PB

use the concept of section formula
where Q is the midpoint of P and B
so, Q={(5+1)/2, (-3-5)/2=(3,-4)