Desperate for help with my math!?

Question

1) In triangle ABC, D(7,3) is the midpoint of Line AB, E(10,9) is the midpoint of Line BC, and F(5,5) is the midpoint of Line AC. Find the coordinates of A, B, and C.

Thanks a bunch! Please explain your answer so that I'll understand how to do this type of problem in the future = )

Answer 1

let point

A be [a,b]

B be [c,d]

C be [e,f]

midpoint formula is always [x,y]= [x1 +x2]/2 , [y1 +y2]/2

so if point D,E, and F are midpoint that means they are represented by the formula above

D, [7,3]= [a+c]/2 , [b +d]/2

             quick arrangement 7= [a+c]/2

                                         14= a+c.............1

                                   and  3= [b +d]/2

                                           6= b+ d ............2

E,[10,9] = [c+e]/2 ,[d+ f]/2

   arrange 20= c+e ........3

               18= d+ f..........4

same case for F,[e+a]/2 , [f+b]/2

                     10=e+ a..........5

                     10=f+b.............6

then do simultaneous equation by substitution.

Answer 2

Um... i dont have graphing paper and i think that would be the easiest way to figure this out. just draw triangle DEF  at the coordinates that you have there and since those are only half way points you should be able to figure it out from there... cake. Hope you figure it out.  

Answer 3

Take any of the midpoints. I'm using D and E. The segments joining the midpoints of the sides of a triangle are parallel and 1/2 the side opposite.

From D to E, x increases by 3 and y increases by 6.

From F, increase x and y in the same way and then decrease in the opposite direction. Since F = (5,5), C = (5+3, 5+6) = (8, 11). A = (5-3, 5-6) = (2,-1). Do the same for the other sides. and B = (12,7)