Question

in what ratio does the point (-4,6) divides the line passing through P(2,5) and Q(x,3)​

Answer 1

Step-by-step explanation:

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 required ratio be m:n

A(−6,10)=(x

1

,y

1

) and B(3,−8)=(x

2

,y

2

)

we have,

(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)=(−4,6)

⇒

m+n

mx

2

+nx

1

=−4

⇒m(3)+n(−6)=−4m−4n

⇒3m−6n=−4m−4n

⇒3m+4m=6n−4n

⇒7m=2n

⇒

n

m

=

7

2

⇒m:n=2:7