the midpoint of AB = (4+22,8−62) = (3, 1)
the midpoint of AC = (4−42,8+42) = (0, 6)
the midpoint of BC = (2−42,−6+42) = (-1, -1)
a line that passes through (3, 1) and (-4, 4) has the equation y=−37x+167
a line that passes through (0, 6) and (2, -6) has the equation y=−6x+6
a line that passes through (-1, -1) and (4, 8) has the equation y=95x+45
The first two lines intersect when
−37x+167=−6x+6−37x+6x=6−167397x=267x=23
And y=−6(23)+6=2
The first two lines intersect at the point (23,2) . So if (23,2) is on the third line, then we know that all three lines pass through (23,2) .
y=95(23)+45=65+45=105=2
So...all three medians pass through (23,2) . Here's a graph of the three lines.