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प्रश्न
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.
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उत्तर
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 : 3 and "y =-3/2 .`
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