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I have a math investigation to do over the holidays. In the last question it asks to investigate the properties of various quadrilaterals (kite, rhombus,rectangle,trapeziums) and consider different aspects about them (equal sides, parallel sides, right angles, bisecting diagonals etc).

What i don't understand with the kite is to answer the question "what information would be needed to determine any unknown coordinates of the vertices or points of intersection of the diagonals." Somehow it all relates to the coordinates of the vertices.

Also i'm having the same problem with the other shapes. Hopefully it's just a simple solution that i've missed.

Any help would be much appreciated. I've been looking online but i can'd find anything that explains :)

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  • $\begingroup$ Here is (math.stackexchange.com/q/2239061) for example a recent question about quadrilaterals that I have been working on, and typical of what you are asking. $\endgroup$ – Jean Marie Apr 23 '17 at 5:12
  • $\begingroup$ Thanks @A.Mahony! As a (relatively) new user, I hope my knowledge can help you and others answer future questions! $\endgroup$ – Toby Mak Apr 23 '17 at 5:28
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To start, the main properties of a kite are that:

  • Two pairs of sides have the same length (1)

  • One pair of angles diagonally opposite each other are equal (2)

  • The diagonals cross at $90º$. (3)

  • Has x-axis and y-axis symmetry (4)

Using property (4), three points are sufficient to create a single kite, or else the symmetry would be broken.

However, with two points, this case is not sufficient. To show this, we have to give a counterexample of two different kites with 2 shared coordinates. For example, this kite and this other kite share coordinates (0,0) and (0,5).

Hope this helps for answering the "determining coordinates" part of your question, and as a good starting point for your investigation.

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