Question

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

Answer 1

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

If the line joining the points A and B are trisected , then the ratios are 3:1 or 1:3

so , when ratio is 3:1

x = {3(-2)+1(4)}/(3+1)

x = -6 + 4 / 4

x = -2 / 4

x = -1/2

and

y = { 3(-3)+1(-1)}/(3+1)

y =( -9 -1)/4

y = = -10/4

y = -5/2

and when we take the ratio as 1:3

x ={ 1(-2)+3(4)}/4

x = (-2+12)/4

x = 10/4

x= 5/2

and ,

y ={ 1(-3)+3(-1)}/4

y=( -3-3)/4

y = -6/4

y = -3/2

So the answer is (-1/2, -5/2) or

(5/2,-3/2)

Answer 2

Answer:

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)]