SOLUTION: Prove or disprove that the diagonals are congruent using coordinate geometry. A(5,7) B(15,3) C(13,-2), D(3,2)

Algebra ->  Geometry-proofs -> SOLUTION: Prove or disprove that the diagonals are congruent using coordinate geometry. A(5,7) B(15,3) C(13,-2), D(3,2)      Log On


   

Question 1137036: Prove or disprove that the diagonals are congruent using coordinate geometry.
A(5,7) B(15,3) C(13,-2), D(3,2)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

A(5,7) B(15,3) C(13,-2), D(3,2)



now use distance formula and prove that the distance AC=BD
AC=sqrt%28%2813-5%29%5E2%2B%28-2-7%29%5E2%29
AC=sqrt%288%5E2%2B%28-9%29%5E2%29
AC=sqrt%2864%2B81%29
AC=sqrt%28145%29
AC=12.0415945787923

BD=sqrt%28%2815-3%29%5E2%2B%283-2%29%5E2%29
BD=sqrt%2812%5E2%2B1%5E2%29
BD=sqrt%28144%2B1%29
BD=sqrt%28145%29
BD=12.0415945787923

=>the diagonals are congruent