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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. image: latex.artofproblemsolving.com/b/c/3/bc36d6a86ebdd87399c8b07d66ec053e8593c264.png

Note that the three medians appear to intersect at the same point. Consider the triangle ABC with A = (3,6), B = (-5,2), and C = (7,-8). (a) Let D, E,F$ be the midpoints of $\overline{BC},$ $\overline{AC},$ $\overline{AB},$ respectively. Find the equations of medians $\overline{AD},$ $\overline{BE},$ and $\overline{CF}.$ (b) Show that the three medians in part (a) all pass through the same point.

 

 

 

I'm really stuck, can somebody help? 

 Aug 28, 2020
 #1
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The coordinates of a centroid G (1.667, 0)

 

AD = √92+ 22         BE = √102+32            CF = √122+82

 

You can do the rest.wink

 Aug 29, 2020
 #2
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How are the coordinates a square root? 

 Aug 29, 2020

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