geometry question

Question

Choose a pair of coordinate points. On a sheet of paper or in a
graphing utility, graph the segment that connects the two points.
Now choose a ratio. Divide the segment into two parts according to
your ratio. Detail your work and tell what the coordinates of all of the
relevant points are.

Answer 1

Choose and graph the two points.

 

Then choose a ratio (note:  1/2 is really too easy).  But, realize that the "midpoint" of a line segment has coordinates:

     ( (x₁+x₂)/2, (y₁+y₂)/2)    [these are the "average" of the x's and the y's]

 

For a line that is 1/3 of the way along the segment, the coordinates of the dividing point are "weighted" averages:

     ( (x₁+2x₂)/3, (y₁+2y₂)/3)