Question

Demonstrate using your own unique example how to divide a segment by a given ratio. Be sure to provide coordinates and a ratio that does not have a numerator or denominator of 1.

Answer 1

Say for example we have segment A with endpoints coordinates of (a,b) and (x,y) and we wish to divide the segment into parts. The ratio of division is assumed to be r. In this case, we identify the first coordinates of the segment next to (a,b) by:

(c,d) = ((x-a)/r + a  , (y-b)/r + b) 

This formula is used including the constant portion of the division of the segment, (x-a)/r. The addition, a, can vary depending on the position of the coordinates to be taken. On the other end, before (x,y), the coordinates should be 
(v,w) = (y - (x-a)/r , z - (y-b)/r )