Question

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

Answer 1

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)]

Answer 2

Answer:

first let the points be

A(4,-1),B(-2,-3)

first let us take the ratio as 1:2 and later 2:1 since its trisection  .

let the point joining A and B be P(x,y)

Step-by-step explanation:

P = (1*-2+2*4/1+2  ,  1*-3+2*-1/1+2)

  = (-2+8/3  ,  -3-2/3)

  =  (6/3  ,  -5/3)

P   =  (2  ,  -5/3)

now let ratio be 2:1

P = (2*-2+1*4/3  ,  2*-3+1*-1/3)

  = (-4+4/3  ,  -6-1/3)

  = (0/3  ,  -7/3)

P = (0 , -7/3)

hence shown ...

hope helpful for you

thank you...