Question

find the ratio in which the points (-3,p) divides the line segment joining the points a(-5,-4) and b(-2,-3) in the ratio k:1​

Answer 1

Step-by-step explanation:

Suppose the point P(−3,p) divides the line segment joining points A(−5,−4)≡(x

2

,y

2

) and B(−2,3)≡(x

1

,y

1

) in the ratio k:1.

Section formula: [x=(

m+n

mx

1

+nx

2

)] and [y=(

m+n

my

1

+ny

2

)]

Then, the coordinates of P are(

k+1

−2k−5

k+1

3k−4

)

But, the coordinates of P are given as (−3,p).

∴

k+1

−2k−5

=−3and

k+1

3k−4

=p

⇒−2k−5=−3k−3and

k+1

3k−4

=p

⇒k=2andp=

k+1

3k−4

⇒k=2andp=

3

2

Hence, the ratio is 2:1 and p=

3

2

.