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 point P divides the line segment AB. Also find the value of x.

Answer 1

Let point P (x, 4) divide line segment AB in the ratio K:1.

Coordinates of A = (−5, 8)

Coordinates of B = (4, −10)

On using section formula, we obtain

`(x,4)=((kxx4+1xx(-5))/(k+1))((kxx(-10)+1xx8)/(k+1))`

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

`rArr(4k-5)/(k+1)=x`........................(1)

`and (-10k+8)/(k+1)=4..................(2)

From equation (2):

− 10K + 8 = 4(K + 1)

⇒ − 10K + 8 = 4K + 4

⇒ 14K = 4

`rArr K =2/7`

Thus, point P divides AB in the ratio `2/7 : ie ., 2:7.`

From equation (1):

`(4xx2/7-5)/(2/7+1)=x`

`(-27/7)/(9/7)=x`

`x=-3`