Given A(4,-3) ,B (8,5) . Find the coordinates of the point that
divides segment AB in the ratio ` 3: 1`

Explanation

A (4,-3) and B(8,5)
Let P(x,y) divide segment AB in the ratio ` 3 : 1` .
`therefore m :n=3 : 1`
Let ` A(x_(1),y_(1) "and " B(x_(2),y_(2))`
Here, ` (x_(1)= 4 , y_(1)) = - 3,(x_(2)= 4" and " ,y_(2))= 5 `
By section formula ,
` x = (mx_(2) + nx_(1))/(m+n)`
` therefore x = (2(8) + 1(4))(3 =1)`
` therefore x = (24 + 4)/(4)`
` therefore x = (28)/(4)`
` therefore x= 7`
` y = (my_(2) + ny_(1))/(m+n)`
` therefore y = (3(5) + 1 (-3))/(3+1)`
` therefore y = (15 -3)/(4)`
` therefore y = (12)/(4)`
` therefore y = 3`
Point (7,3) divides segment AB is the ` 3 :1` .