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

Answer:

$(\frac{37}{11},\frac{77}{11}  )$

Step-by-step 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

$(\frac{mx2+nx1}{m+n} ,\frac{my2+ny1}{m+n} )$

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,

$(\frac{6*7+5*-1}{11} ,\frac{6*7+5*7}{11} )$

$(\frac{37}{11},\frac{77}{11}  )$