Question

find the coordinates of the points of trisection (I. e.,points dividing the line segment ,in three equal parts )of the line segment joining the point (2,-2)and (-7,4)​

Answer 1

Step-by-step explanation:

Given:- A line segment joining the points A(2,−2) and B(−7,4).

Let P and Q be the points on AB such that,

AP=PQ=QB

Therefore, 

P and Q divides AB internally in the ratio 1:2 and 2:1 respectively.

As we know that if a point (h,k) divides a line joining the point (x1,y1) and (x2,y2) in the ration m:n, then coordinates of the point is given as-

(h,k)=(m+nmx2+nx1,m+nmy2+ny1)

Therefore,

Coordinates of P=(1+21×(−7)+2×2,1+21×4+2×(−2))=(−1,0)

Coordinates of Q=(1+22×(−7)+1×2,1+22×4+1×(−2))=(−4,2)

Therefore, the coordinates of the points of trisection of the line segment joining A and B are