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.

Advertisement Remove all ads

#### 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 .`

Concept: Coordinate Geometry

Is there an error in this question or solution?

#### APPEARS IN

Advertisement Remove all ads