SOLUTION: Please...please help...I am so stuck! Points R (-9, -3), S(-5, 5) and T (-2, -2) are the vertices of a triangle. Segments RA, SB and TC are the medians of RST. Determine the coo

Question 704146: Please...please help...I am so stuck!
Points R (-9, -3), S(-5, 5) and T (-2, -2) are the vertices of a triangle. Segments RA, SB and TC are the medians of RST. Determine the coordinates of A, B, and C. What do you notice about the there medians?
Thank you!
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The medians connect one vertex to the midpoint of the other side

RA is a median, so A must be the midpoint of ST, and
the coordinates of A are the averages of the coordinates of S and T:
and .

Similarly, the coordinates of B are
and .

And the coordinates of C are
and .

I think you were expected to graph the whole thing,and get something like this:

When you split a triangle in two with a median,
the two pieces are triangles with the same area.
They have bases (the split side) of the same length,
and the height from that base to their shared vertex is the same.
The medians meet at the "center of gravity" of the triangle.

If you draw a triangle, cut it out, and draw the medians,
you can stick a pin anywhere in the triangle,
let it dangle freely (maybe the pin hole needs to get a little larger),
and the point where the medians cross should hang directly below the pin.

That point has a fancy name, you can look it up.
Is it incenter, circumcenter, centroid, orthocenter, or something else?
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