Question

If the point P ( 10 , − 21 ) divides the line segment joining A and B ( 18 , − 45 ) in the ratio 1 : 8 , find the coordinates of A .

Answer 1

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

)

Given: A(1,3)≡(x

1

,y

1

) and B(4,6)≡(x

2

,y

2

)

m

1

=2 and m

2

=1

Let the co-ordinates of P be (x,y)

∴x=

2+1

2×4+1×1

⇒x=

3

8+1

=

3

9

=3

∴y=

1+2

2×6+1×3

⇒y=

3

12+3

=

3

15

=5

∴P=(3,5).