The coordinates for a rhombus are given as (2a, 0), (0, 2b), (–2a, 0), and (0, –2b). Write a plan to prove that the midpoints of the sides of a rhombus determine a rectangle using coordinate geometry. Be sure to include the formulas.
The midpoints of the sides are: M ( (2a+0)/2 , (2b+0)/2 ) = ( a , b ) N ( (-2a+0)/2 , (2b+0)/2 ) = ( - a, b ) P ( (-2a+0)/2, ( -2b+0)/2 ) = ( - a, - b ) Q ( (2 a+0)/2) , (-2b+0)/2 ) = ( a , - b ) The midpoints of a rhombus determine a rectangle.
