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.

Answer 1

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 .`