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.

Question

anonymous · Answer

attachment

radar · Answer

Your diagram is excellent, and shows that indeed the rectangle is formed.  The width being 2a and the height being 2b.

anonymous · Answer

Thanks! Can you help me with the formulas?:)

radar · Answer

Using the diagram and connecting the dots.  The top horizontal line segment is y=b and the segment is the distance of the endpoints which is a-(-a) = 2a, the same goes for the bottom horizontal segment.  The bottom is y=-b

The vertical segments on the left and right would be x=-a (left side) and x=a on the right.
The distance from the endpoints is b-(-b)=2b

radar · Answer

So the rectangle formed has the dimensions of 2a X 2b

radar · Answer

Since the lines are horizontal and vertical they form 90 degrees angles where they intersect.  A characteristic of rectangle.

radar · Answer

Thats all that I can come up with, hope it is enough.

anonymous · Answer

Yes, thank you so much!:) You've been such as big help!:)

radar · Answer

NP, good luck with your studies.