SOLUTION: prove that quadrilateral GHIJ with the vertices G(-2,2), H(3,4), I(8,2), and J(3,0) is rhombus

Algebra ->  Parallelograms -> SOLUTION: prove that quadrilateral GHIJ with the vertices G(-2,2), H(3,4), I(8,2), and J(3,0) is rhombus       Log On


   

Question 1153027: prove that quadrilateral GHIJ with the vertices G(-2,2), H(3,4), I(8,2), and J(3,0) is rhombus
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Diagonal GI lies on the horizontal line y=2; diagonal HJ lies on the vertical line x=3. So the two diagonals are perpendicular to each other.

The intersection of the two diagonals is the midpoint of both diagonals.

A quadrilateral whose diagonals are perpendicular and bisect each other is a rhombus.

Of course many other methods can be used to do the proof; this one looked easiest to me....