Question

4.
Find the ratios in which the points
1.P (2.1)
2.Q(-1. - 8) divide the line segment joining the points A(1, 2) and B(4,7)
​

Answer 1

Answer:

Using the section formula, if a point (x,y) divides the line joining the points (x

1

,y

1

) and (x

2

,y

2

) in the ratio m:n, then

(x,y)=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

Let the point P(x,y) divides AB in the ratio m:n.

A(−2,1) and B(1,4) are the given points.

Given m:n=2:1

∴x

1

=−2,y

1

=1,x

2

=1,y

2

=4,m=2 and n=1

∴ By Section formula

x=

2+1

2×1+1×−2

∴x=

3

2−2

∴x=

3

0

∴x=0

And

y=

2+1

2×4+1×1

∴y=

3

8+1

∴y=

3

9

∴y=3

Hence the co-ordinates of point P are (0,3).