Find the ratio in which the pint (-3, k) divide the join of A(-5, -4) and B(-2, 3),Also, find the value of k.

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#### Solution

Let the point P (-3, k) divide the line AB in the ratio s : 1

Then, by the section formula :

`x = (mx_1 + nx_1) /(m+n) , y= (my_2 +ny_1)/(m+n)`

The coordinates of P are (-3,k).

`-3=(-2s-5)/(s+1) , k =(3s-4)/(s+1)`

⇒-3s-3=-2s-5,k(s+1)=3s-4

⇒-3s+2s=-5+3,k(s+1) = 3s-4

⇒-s=-2,k(s+1)= 3s-4

⇒ s =2,k(s+1)=3s-4

Therefore, the point P divides the line AB in the ratio 2 : 1.

Now, putting the value of s in the equation k(s+1)=3s-4 , we get:

k(2+1)=3(2)-4

⇒ 3k=6-4

⇒ 3k = 2⇒k=`2/3`

Therefore, the value of k`= 2/3`

That is, the coordinates of P are `(-3,2/3)`

Concept: Coordinate Geometry

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