Question

find the ratio in which the point p x ,2 divides the lines segment joining the point a 12,5 b4,_3 find x

Answer 1

is your question ----> find the ratio in which the point p(x, 2) divides the lines segment joining the point a(12,5) b(4, -3) find x ?

solution :- use formula, $y=\frac{\lambda y_2+y_1}{\lambda+1}$

where, y = 2, $y_2=-3,y_1=5$ and $\lambda$ is the ratio in which the given point divides the line segment joining the point a and b.

now, 2 = $\frac{-3\lambda+5}{\lambda+1}$

or, 2$\lambda$ + 2 = -3$\lambda$ + 5

or, $5\lambda=3\implies\lambda=3/6$

so, point P divides line segment ab in the ratio of 3 : 5

now, applying $x=\frac{\lambda x_2+x_1}{\lambda+1}$

so, x = (3/5 × 4 + 12)/(3/5 + 1)

= (12 + 60)/8 = 9

hence, x = 9

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.