# 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. - Mathematics

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 .

Concept: Coordinate Geometry
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 28