Question

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?

Answer 1

G(3, 1), H(2, 3)

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)