Question

In what ratio does the point C(4, 5) divide the join of A(2, 3) and B(7, 8)?

Answer 1

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.