Find the possible pairs of coordinates of the fourth vertex D of the parallelogram, if three of its vertices are A(5, 6), B(1, -2) and C(3, -2).

Answer: D(7, 6) if the parallelogram is ABCD; the other possible positions are D(3, 6) and D(-1, -10).

Diagonals of a parallelogram bisect each other, so the sum of the coordinates of opposite vertices is equal.

Parallelogram ABCD (AC and BD are diagonals): \(D=A+C-B=(5+3-1,\ 6-2+2)=(7,6)\).

With AB as a diagonal: \(D=A+B-C=(5+1-3,\ 6-2+2)=(3,6)\).

With BC as a diagonal: \(D=B+C-A=(1+3-5,\ -2-2-6)=(-1,-10)\).

The textbook answer key lists (7, 6) and (3, 6).