Find coordinates of A, B, and C please! or just help figure out the problem.?

Question

In triangle ABC, D(7,3) is the midpoint of AB, E(10,9) is the midpoint of BC, and F(5,5) is the midpoint of AC

Answer 1

Graph it on a piece of paper.  pythagorean theorem.  Each coordinate gives a clue as to the coordinates of the endpoints.  I'd do the rest but I dont feel like graphing it.  

Answer 2

This can be done wholly algebraically.  The notation is going to be a mess here, so bear with me.

Let A be (a1, a2).  B is (b1, b2) and C is (c1, c2).  We have six unknowns, so we need six equations.

We know the midpoint of AB is (7, 3).  That tells us that

(a1 + b1)/2 = 7

(a2 + b2)/2 = 3

We know the midpoint of BC is (10, 9):

(b1 + c1)/2 = 10

(b2 + c2)/2 = 9

And the midpoint of AC is (5, 5)

(a1 + c1)/2 = 5

(a2 + c2)/2 = 5

Six equations, six unknowns.  That can be solved.  It's easier than it looks, though, because we actually have two sets of coupled equations.  We have three equations in three unknowns for the x coordinates, and three equations in three unknowns for the y coordinates.

I will leave the solution to you.