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The diagonals of quadrilateral EFGH intersect at D(?3,4). EFGH has vertices at E(3,7) and F(?4,5). What must be the coordinates of G and H to ensure that EFGH is a? parallelogram?

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sqdancefan

Answer:

  G(3, 1), H(2, 3)

Step-by-step explanation:

When D is the midpoint of EG, it means ...

  D = (E + G)/2

or

  G = 2D -E = 2(3,4) -(3,7) = (2·3-3, 2·4-7) = (3, 1)

Likewise, H is ...

  H = 2D -F = 2(3,4) -(4,5) = (2·3-4, 2·4-5) = (2, 3)

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