Full Question: The coordinates for a rhombus are given (2a, 0), (0, 2b), (-2a, 0), (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.

Question

Full Question: The coordinates for a rhombus are given (2a, 0), (0, 2b), (-2a, 0), (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.
 
Image Description: The image looks like a rhombus. The very top vertex ( (0,2b), the left vertex ( (-2a, 0) ), the bottom vertex ( (0,-2b, the right vertex ( (2a,0) ). There are four more vertexs on the figure. (-a,-b) is in the middle of (-2a, 0), (a,-b) is in the middle of (0,-2b) and (2a,0), (a, b) is in the middle of (0,2b) and (2a,0), and finally (-a,b) is in the middle of (0,2b) and (-2a,0) 
 
I'm not really good with proofs, so I don't really know where to even start. So if someone could please help me answer this and go into detail so I understand what I'm doing, that would be awesome! Thank you to whoever helps.
 
*Note*
 
If you need any more details about the image, please let me know

dabi · Accepted Answer

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.

you know, you know Soobin? · Answer

I'm going to trust you dabi.