The midsegment of a triangle is a line connecting the midpoints of two sides of the triangle. So a triangle has 3 midsegments. Since you want the midsegment that's parallel to LN, we need to select the midpoints of LM and MN. The midpoint of a line segment is simply the average of the coordinates of each end point of the line segment. So:
Midpoint LM:
((0+6)/2, (5+4)/2) = (6/2, 9/2) = (3, 4.5)
Midpoint MN:
((6+0)/2, (4+2)/2) = (6/2, 6/2) = (3, 3)
So the desired end points are (3, 4.5) and (3, 3)</span>
