Question

Find the ratio in which point P(-1,4) lying on the line segment joining points A(-3,10) and B(6,-8) divides It.​

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 ratio be m:n

Then,

m+n

mx

2

+nx

1

=−1

⇒

m+n

6m+3n

=−1

⇒6m−3n=−m−n

⇒7m=2n

⇒

n

m

=

7

2

⇒m:n=2:7

Now,

m+n

my

2

+ny

1

=y

⇒

2+7

2(−8)+7(10)

=y

⇒−16+70=9y

⇒9y=54

⇒y=

9

54

=6

Answer 2

Answer:

Ratio in which point P(-1,4) lying on the line segment joining points A(-3,10) and B(6,-8) divides it -

The solution is attached.