Question

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

Answer 1

Answer:

Let the point P(x,4) divide the line segment joining the points A(-5,8) and B(4,-10) in the ratio k:1.

So, by applying Section formula,

(4k-5/k+1, -10k+8/k+1) = (x,4)

By comparing the corresponding coordinates,

-10k+8/k+1=4

⇒4k+4=-10k+8

⇒14k=4  ⇒ k=2/7

Also, 4k-5/k+1 = x → (1)

Substituting k=2/7 in Eq. (1),

x=8/7-5/2/7+1 ⇒ x=-3

Hence, the required ratio is 2:7

The value of x is -3.

Hope it helps you

Answer 2

Answer:

Let the point P(x,4) divide the line segment joining the points A(-5,8) and B(4,-10) in the ratio k:1.

So, by applying Section formula,

(4k-5/k+1, -10k+8/k+1) = (x,4)

By comparing the corresponding coordinates,

-10k+8/k+1=4

⇒4k+4=-10k+8

⇒14k=4  ⇒ k=2/7

Also, 4k-5/k+1 = x → (1)

Substituting k=2/7 in Eq. (1),

x=8/7-5/2/7+1 ⇒ x=-3

Hence, the required ratio is 2:7

The value of x is -3.