Question

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

Answer 1

Let P and Q be the points of trisection of line joining the points A(4,1) & B(-2,-3). Now, P divides AB in the ratio 1:2 and Q divides AB in the ratio 2:1. Hence, the two points of trisection are P(−1,0) and (−4,2).

Answer 2

Let A(4,-1) be the first point and B(-2,-3) be the second point and P and Q be the the internally trisecting point.

Let AB=PQ=QB=k

PB=PQ+QB=2k

and AQ=AP+PQ=2k

>AP:PB=1:2

and AQ:QB=2:1

P divides a b internally in ratio 1:2 while Q divides internally in the ratio 2:1. Does coordinates of p and q are

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

and similarly

Q[0,(-7/3)]