Point P(x, 4) lies on the line segment joining the points A(-5, 8) and B(4, -10). Find the ratio in which point P divides the line segment AB. Also, find the value of x.(CBSE 2011)

Let P divides AB in a ratio r: 1.

∴ AP : BP = r : 1

Now, coordinates of P will be .

But, coordinates of P are (x, 4).

So, equating the x coordinate and y coordinate separately, we get:

= x and = 4

On solving the second equation, we get:

-10r + 8 = 4r + 4

⇒ 14r = 4

⇒ r = 2/7

Therefore, r :1 will be equal to 2/7 : 1 = 2 : 7

Thus, the point P divides AB into a ratio 2 : 7

Also, on solving the first equation, we get:

4r – 5 = (r + 1)x

⇒ 4(2/7) – 5 = [(2/7) + 1]x

⇒ 8 – 35 = 9x

⇒ - 27 = 9x

⇒ x = - 3

Therefore, the ratio is 2 : 7 and the point P is (- 3, 4).