Question

find the coordinate of the points which divides the line segment joining A(5,-6)and B(7,-8)into four equal points

Answer 1

Heya !!!


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

Let P and Q be the points of AB which Divides AB in four Equal parts.

Then, P Divides AB in ratio 1 : 3

M1 = 1 and M2 = 3

And,

A(5 , -6) and B(7,-8)

Here,

X1 = 5 , Y1 = -6 and X2 = 7 , Y2 = -8

So,

The coordinates of P are ( M1X2+M2X1/M1+M2 , M1Y2 + M2Y1/ M1+M2)

=> P ( 1 × 7 + 3 × 5/ 1+3 , 1 × -8 + 3 × -6 / 1+3)

=> P(7 + 15/4 , -8 - 18 /4)

=> P ( 22/4 , -26/4)

=> P(11/2 , -13/2)

And,

Q Divides AB in ratio 2:2 = 1:1

M1 = 1 and M2 = 1

A(5,-6) and B(7,-8)

Here,

X1 = 5 , Y1 = -6 and X2 = 7 ,Y2 = -8

So,

Coordinates of Q are Q( M1X2 +M2X1/ M1+M2 , M1Y2+ M2Y1/ M1+M2)

=> Q( 1 × 7 + 1 × 5/ 1+1 , 1 × -8 + 1 × -6 / 1+1)

=> Q ( 7 + 5/2 , -8 -6/2)

=> Q( 12/2 , -14/2)

=> Q(6,-7)

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