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Question
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
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