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Question
If the point `P (1/2,y)` lies on the line segment joining the points A(3, -5) and B(-7, 9) then find the ratio in which P divides AB. Also, find the value of y.
Solution
Let the point `P (1/2,y)` divides the line segment joining the points A(3, -5) and B(-7, 9) in the ratio k : 1 .Then
` (1/2, y ) = ((k(-7)+3)/(k+1) , (k(9)-3)/(k+1))`
`⇒ (-7k +3)/(k+1) = 1/2 and (9k-5)/(k+1) = y `
`⇒ k+1 = - 14k +6 ⇒ k= 1/3`
`"Now, substituting " k = 1/3 "in" (9k-5)/(k+1) = y `, we get
`(9/3-5)/(1/3+1) = y ⇒ y = (9-15)/(1+3) = -3/2`
`"Hence, required ratio is 1:3and " y =3/2 .`
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