Question

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

Answer 1

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