Question

P( x , 4 ) lies on the line segment joining A ( -5 , 8 ) and B (4 , -10 ). Find the ratio in which P divides AB. Also find x.

Answer 1

Answer:

ANSWER

Given: A line segment joining the points A(3,−1) and B(8,9) and another line x−y−2=0.

Let a point P(x,y) on the given line x−y−2=0 divides the line segment AB in the ratio m:n

To find: ratio m:n

x=

m+n

mx

2

+nx

1

=

m+n

m×8+n×3

=

m+n

8m+3n

and y=

m+n

my

2

+ny

1

=

m+n

m×9+n×(−1)

=

m+n

9m−n

Since point P lies on x−y−2=0, so

m+n

8m+3n

−

m+n

9m−n

−2=0

m+n

8m+3n

−

m+n

9m−n

=2

8m+3n−9m+n=2m+2n

−m+4n=2m+2n

−m−2m=+2n−4n

−3m=−2n

n

m

=

−3

−2

=

3

2

The required ratio is 2:3.