Find the ratio in which point P (k,7) divides the segment joining
A(8,9) and B(1,2) .

Explanation

A (8,9) , B (1,2) and P(k,7) .
Let P divide the seg AB in the ratio ` m: n`
Let P divide the seg AB in the ratio ` m: n`
By section furmula ,
` y = (my_(2) + ny_(1))/(m+n)`
` therefore 7= (m(2) + n(9))/(m+n)`
` therefore 7 = (2m + 9n)/(m+n)`
` therefore 7(m+n) = 2m + 9n`
`therefore 7m + 7n = 2m + 9n`
` therefore 7m - 2m = 0n - 7n`
` therefore 5m = 2n`
` therefore (m)/(n) = (2)/(5) therefore m:n = 2 :5`
The ratio in which point P divides seg AB os ` 2 : 5 ` .