Question

In what ratio does the point (-4,6) divide the line segment joining the points A(-6,10) and B(3,-8)?

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Answer 1

Answer:

Step-by-step explanation:

Using section formula

x=(m1x2+m2x1)/(m1+m2)

Let m1=k

m2=1

So,-4= (3k-6)/k+1

on simplification we get k= 2/7

that is m1:m2= 2:7

Hence the ratio is 2:7 Ans.

Answer 2

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 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

$\pink{⇒m:n=2:7}$