Question

What ere the coordinates of the point on the directed line segment from (-1,7) to (7,7) that partitions the segment into a ratio of 6 to 5?​

Answer 1

`((37)/(11),(77)/(11)  )`

Explanation:

Given two points are (-1,7) and (7,7).

We are told to find a point which is in between them at a ratio of 6:5.

Formula for calculating a point at distance of ratio m:n is given by

`((mx2+nx1)/(m+n) ,(my2+ny1)/(m+n) )`

where
`(x1,y1),(x2,y2)` are the inital and final points.

`(x1,y1)=(-1,7)\\\\(x2,y2)=(7,7)`

also m:n=6:5 ,

by substituting all the values we get,

`((6*7+5*-1)/(11) ,(6*7+5*7)/(11) )`

`((37)/(11),(77)/(11)  )`