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

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.

Answer 2

use section fourmula

p(x,y)=(4m-5n/m+n,-10+8n/m+n)

y coordinate 4=-10+8n/m+n; m/n=2/7

w.k.t x=4m-4n/m+n

= 4(m/n)-5/m/n+1

x=8-35/9;x=-3

p(-3,4)