Find the ratio in which point P(6,7) divides the segment joining
A(8,9) and B(1,2) by completing the following activity .

Explanation

Let P divide the segment AB in
the ratio ` m:n`
`A (8,9) = (x_(1)y_(1))`
` B(1,2) = (x_(2) ,x_(2))`
` P(6,7) = (x,y)`
By section formula
` 7= (m square+ n(9))/(m+n) `
` therefore 7m + 7n = square + 9n`
` therefore 7m - square = 9n - square`
` therefore square = 2n`
` therefore (m)/(n) = square`
Let P divide the segment AB in
the ratio ` m:n`
` A (8,9) = (x_(1) y_(1))`
` B (1,2) = (x_(2) ,x_(2))`
P(6,7) = (x,y)
By section formula
`7=(m2+n9)/(m+n)`
`:. 7m+ 7n=2m+9n`
`:. 7m-2m=9n-7n`
`:. 5m=2n`
`:. (m)/(n)=(2)/(5)`