(Q5)Find the coordinates of the points of trisection of the line segment joining the points A(2,-2) and (-7,4).

Answer

Let P and Q be the points of trisection AB i.e. AP=PQ=QB=k

therefore, P divides AB internally in the ratio 1:2

Therefore the coordinates of P are(By applying the section formula)

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

= (
1(-)+2()
1+2
 ,
1()+2(-)
1+2
)
= (
-
3
 ,
3
)

(-,)

Now Q also divides AB internally in the ratio 2:1

So, the coordinates of Q are

(
2(-)+1()
2+1
 ,
2()+1(-)
2+1
)
= (
-
3
 ,
3
)

(-,)

Therefore the coordinates of the points of trisection of the line segment are P(-,) and Q(-,).