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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.
Solution
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`
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