# In What Ratio Does the Point P(2,5) Divide the Join of a (8,2) and B(-6, 9)? - Mathematics

In what ratio does the point P(2,5) divide the join of A (8,2) and B(-6, 9)?

#### Solution

Let the point  P (2,5) divide AB in the ratio k : 1

Then, by section formula, the coordinates of P are

 x= (-6k+8)/(k+1) , y = (9k+2)/(k+1)

It is given that the coordinates of P are ( 2,5).

⇒ 2= (-6k +8) /(k+1) , 5 =(9k +2) /(k+1)

⇒ 2k + 2 = -6k +8 , 5k +5 = 9k +2

⇒ 2k + 6k = 8 -2 , 5-2=9k-5k

⇒ 8k = 6, 4k =3

⇒ k = 6/8, k = 3/4

⇒ k = 3/4  in each case..

Therefore, the point P (2,5)  divides AB in the ratio3:4

Concept: Coordinate Geometry
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 13