Iam having a total mind blank right now.
write a coordinate proof for the following theorem. if a quadrilateral is a kite then it's diagonals are perpendicular.

Theorem:  If a quadrilateral is a kite then it's diagonals are perpendicular.

Proof:- In kite WXYZ, let O(a,b) be the intersection point of the diagonals .

Also the distance formula is given by ,

Distance from

In ΔWOX,

OX=a  [since the coordinate of x changes but not y, thus the distance from O to X=a]

WO= 3b  [since the coordinate of y changes but not x, thus the distance from O to W = 4b-b=3b]

WX=

We can see that

[By the converse of Pythagoras theorem]

⇒ The diagonals are perpendicular.

Hence proved.

irrational, cannot