(Q24) Find the coordinates of the points of trisection of the line segment joining(4,-1) and (-2,-3).

Answer

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

Let P and Q be the points of trisection of AB then AP=PQ=QB

ABPQ(4,-1)(-2,-3)

P divides AB internally in the ratio 1:2

P(x,y) = (
m1x2+m2x1
m1+m2
 ,
m1y2+m2y1
m1+m2
)

= (
1×(-)+2×
1+2
 ,
1×(-)+2×(-)
1+2
)
= (
3
 ,
-
3
)
P(x,y)= (,
-
3
)

Also, Q divides AB in the ratio 2:1 internally

Q(x,y)= (
2×(-)+1×
2+1
 ,
2×(-)+1×(-)
2+1
)
= (,
-
3
)
Q(x,y)= (0,
-
3
)