How can I prove that a quadrilateral formed by connecting the midpoints of a kite is a rectangle in coordinate geometry? I worked something out but I don't know.

This is what I have, no judgement.

lets say that hypothetically the vertices of this kite are (-2a,0) (2a,0)(0,2b) and (0,-2c) which would mean the midpoints of this kite are (a,b)(-a,b)(a,-c) and (-a,-c) which would connect to be a rectangle and its vertices.

Question

How can I prove that a quadrilateral formed by connecting the midpoints of a kite is a rectangle in coordinate geometry? I worked something out but I don't know. 

This is what I have, no judgement.

lets say that hypothetically the vertices of this kite are (-2a,0) (2a,0)(0,2b) and (0,-2c) which would mean the midpoints of this kite are (a,b)(-a,b)(a,-c) and (-a,-c) which would connect to be a rectangle and its vertices.

anonymous · Answer

What do you think?