A median of a triangle is a line segment joining a vertex of a triangle to the midpoint of the opposite side. The three medians of a triangle are drawn below.
https://latex.artofproblemsolving.com/b/c/3/bc36d6a86ebdd87399c8b07d66ec053e8593c264.png
Note that the three medians appear to intersect at the same point! Let's try this out with a particular triangle. Consider the triangle ABC with A=(3,6),B=(-5,2) , and C=(7,-8) .
(a) Let D, E ,F be the midpoints of BC, AC, AB respectively. Find the equations of medians AD, BE, and CF.
(b) Show that the three medians in part (a) all pass through the same point.
Somebody please, thank you. Cphill?
+934 a. The equation of AD I get y= -3/2x+5/2, for BE I get y= -3/10x+1/2, and for CF I get y= -3/2x+5/2.
b. If you set each equation to equal each other, you'll find the point they intersect at. After finding where they intersect, you'll find that they intersect each other at the same point.
*Sorry for the vague explanation
Hope it helps!
