Question

The diagonals of quadrilateral ABCD intersect at E(0,2). ABCD has vertices at A(1,6) and B(-2,4). What must be the coordinates of C and D to ensure that ABCD is

a parallelogram?

Answer 1

C = (-1, -2)

D = (2, 0)

Explanation:

You want the coordinates of points C and D in parallelogram ABCD such that point E(0, 2) is the intersection of the diagonals. Given points are A(1, 6) and B(-2, 4).

Parallelogram

The diagonals of a parallelogram bisect each other. This means the point of intersection of the diagonals is the midpoint of each:

E = (A +C)/2 . . . . . . . . . . . . . . . E is the midpoint of AC

C = 2E -A = 2(0, 2) -(1, 6)

C = (-1, -2)

and

D = 2E -B = 2(0, 2) -(-2, 4) . . . . . using the same pattern

D = (2, 0)