Geometry

I have no idea how to solve this problem. The question says:
Determine whether the points A(4,5), B(-3,3), C(-6,-13) and D(6,-2) are the vertices of a kite. Explain your answer.
Can you please help me with the steps to solve it and understanding it.

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  1. Graph all the points given on the xy-plane. If you get a picture of a KITE, then the answer is yes.

    Of course, I graphed all the points for you and determined that the given 4 points form a picture of a kite.

    Done!

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  2. first draw it.
    It looks kind of like a kite with the tip at A, the tail at C, the wing tips at B and D
    let's see if AC is perpendicular to BD
    slope C to A = (5+13)/(4+6) = 18/10 = 1.8
    slope B to D = (-2-3)/(6+3) = -5/9
    ah ha, slope 2 = -1/slope 1, they are perpendicular
    This sure looks like a kite.
    the final proof would be to find the intersection P of the lines BD and AC and see if BP = PD

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  3. Thanks! =)
    But one more question about this...
    I looked in the back of the book for help because that's where all the answers are (No I don't use it to cheat. Knowing the answers helps me to figure how the steps to solve it.) and it said something about slopes and using the distance formula. Am I suppose to use that instead?

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  4. geometric concept is modeled by the beam of a flashlight

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