Question

The diagonals of quadrilateral EFGH intersect at D(1,3). EFGH has vertices at E(2,6) and F(-4,5). What must be the coordinates of G and H to ensure that EFGH is

a parallelogram?

Answer 1

• G(0, 0), H(6, 1)

Explanation:

The diagonals of a parallelogram bisect each other.

Point D is the midpoint of both diagonals.

Endpoint of EG is point G with coordinates (x, y):

• (2 + x)/2 = 1 ⇒ 2 + x = 2 ⇒ x = 0
• (6 + y)/2 = 3 ⇒ 6 + y = 6 ⇒ y = 0
• G = (0, 0)

Endpont of FH is point H with coordinates (x, y):

• (-4 + x)/2 = 1 ⇒ - 4 + x = 2 ⇒ x = 4 + 2 ⇒ x = 6
• (5 + y)/2 = 3 ⇒ 5 + y = 6 ⇒ y = 6 - 5 ⇒ y = 1
• H = (6, 1)