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13 November, 05:27

Alana is writing a coordinate proof to show that the diagonals of a rectangle are congruent. she starts by assigning coordinates to a rectangle as shown. then she uses the coordinates to write and simplify expressions for the lengths of the diagonals.

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  1. 13 November, 05:36
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    The solution for the problem is:

    d (S, P) = √ (0-0) ^2 + √ (b-0) ^2

    d (S, P) = √b^2

    d (S, P) = b

    so we know that, SP = b

    d (P, Q) = √ (a-0) ^2 + √ (b-b) ^2

    d (P, Q) = √a^2

    d (P, Q) = a

    so

    PQ = a

    SQ = c^2 = a^2 + b^2

    SQ = √ (a^2 + b^2)

    Therefore, the answer is √ (a^2 + b^2).
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