Question 1004794
{{{graph(300,200,-10,10,-10,10,(4x/3)-(28/3),(-x/4)+(13/2),-5x+16)}}}
Midpoints of each side is the average of the x values and y values of each end.
The midpoints are 
(7,0),(6,5),(3,1)
The midpoint of the triangle is 2/3s the length of the median.
Find one vertex, and go 2/3s the way to the midpoint of the opposite side.  Directions matter. Start at the point, and take 2/3s the x value and 2/3s the y-value.
The easiest one is 2/3s from (2,6) to (7,0)
The x-valueis  2/3s from 2 to 7.  The distance is 5, and 2/3 of that is 10/3, or 3 1/3.  So the x-value is 5 1/3 or 16/3. The y-value is 2/3 s from 6 to 0, or 2/3 of 6=4.  The y-value is 2.
The midpoint is (16/3,2).
This will work for the other two points to the opposite side midpoint.