Question

Find the ratio in which the point P(x,2) divides the line segment joining the points A(12,5)

and B(4,-3). Also find the value of x.​

Answer 1

Answer:

Step-by-step explanation:

let be ratio m;n

therefore x = mx2+nx1/m+n

lly for y = my2+ny1/m+n

∴ 2=  m(-3)+n(5)/m+n

2m+2n =   -3m+5n

⇒2m +3m +2n - 5n

5m - 3n

5m = 3n

ratio 3 :5

for  x

x = mx2+nx1/m+n

⇒ x = 3(12) +5(x)/3+5

⇒ 8x = 36+5x

8x-5x = 36

3x = 36

x = 12

i hope this will help u

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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.