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Question
In what ratio does the point C (4,5) divides the join of A (2,3) and B (7,8) ?
Solution
Let the required ratio be k : 1
Then, by section formula, the coordinates of C are
`c((7k+2)/(k+1) , (8k+3)/(k+1))`
Therefore,
`(7k+2)/(k+1) =4 and (8k+3)/(k+1) =5 [∵C (4,5) is given]`
`⇒7k + 2 =4k + 4 and 8k +3=5k +5 ⇒ 3k =2`
`⇒ k = 2/3`in each case
So, the required ratio is `2/3 `: 1 , which is same as 2 : 3.
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