Question

Find the ratio in which point P(x,2) divides the join of A (12,5) B(4,-3)

Answer 1

y=my2+ny1/m+n
2=m(-3)+n(5)/m+n
2m+2n=-3m+5n
2m+3m=5n-2n
5m=3n
m/n=3/5
so, the ratio is 3:5

Answer 2

Answer:

Let the required ratio be K:1.

Then, By section formula,the Coordinates of P are :

P ( 4K + 12/K + 1 , -3K + 5 / K + 1 )

But , this points is given as P ( x , 2).

Therefore,

⇒ -3K + 5 / K + 1 = 2

⇒ -3K + 5 = 2K + 2

⇒ 5K = 3

⇒ K = 3/5.

So, the required ratio is 3:5.