Question

how do you find the coordinates of triangle ABC if only given the coordinates of their midpoints D(4,1)E(-2,3)F(1,-4)...using analytic geometry

Answer 1

rather  long & round about:

Mide points av all sides=tangent tu serkel inside the triangel

Draw triangel tween midpoints=chord av the inside serkel

perpendikular bisekters av chords go thru senter av serkel, so yu kan find the senter,

then radius av inside serkel.

Sides save original triangel tangent tu this serkel, so get slope av line from serkel

senter tu tangent point.  Triangel side is perpendikular tu this.