Question

Find the co ordinate of point of trisection of line segment joining the point A(5,minus6) and B(minus4,3)

Answer 1

Hiiii friend,

A-------P------Q--------B

A(5,-6) and B(-4,3)

Let P and Q be the points of trisection of AB

Then, P Divides AB in ratio of 1:2.


Therefore,

M1 = 1 and M2= 2


By sectional formula,

the coordinates of P are

P(M1X2+M2X1/M1+M2)

P(1 × -4 + 2 × 5/1+2 , 1 × 3 + 2 × (-6) / 1+2)

P(-4+10/3 , 3-12/3) = P(6/3 , -9/3)

P(2,-3)

Also , Q Divides AB in traffic ratio of 2:1

Therefore,

M1 = 2 and M2= 1

By sectional formula,



the coordinates of Q are:

Q(M1X2+M2X1/M1+M2)

Q(2 × -4 + 1 ×5 / 2+1 , 2 × 3 + 1 × (-6) / 2+1)

Q(-8+5/3 , 6 -6 /3)

Q(-3/3 , 0/3) = Q(-1,0)

Hence,

The points of the trisection of AB are P(2,-3) and Q(-1,0)

HOPE IT WILL HELP YOU....... :-)