Question

in what ratio does the points p(2,5)divide the line segment joining a(8,2) and ;(-6,9)​

Answer 1

Answer:

Given: P(2,5) divides the line segment joining the points A(8,2) and B(−6,9).

Let P divides the AB in the ratio m:n

2=

m+n

mx

2

+nx

1

=

m+n

m(−6)+n×8

2m+2n=−6m+8n

2m+6m=8n−2n

⇒8m=6n

n

m

=

8

6

=

4

3

Ratio =3:4.

Answer 2

Answer:

Given: P(2,5) divides the line segment joining the points A(8,2) and B(−6,9).

Let P divides the AB in the ratio m:n

2=m+nmx2+nx1=m+nm(−6)+n×8

2m+2n=−6m+8n

2m+6m=8n−2n

⇒8m=6n

nm=86=43

Ratio =3:4.