The area of a square is 81. One corner of the square is at the point (5, -4). Which of these points could be an adjacent corner of the square?

- (5 – 6√2, 1)
- (-8, 6√2 – 4)
- (2, 6√2 – 4)
- (6√2 – 5, -1)
- (8, 4-6√2)

The sides of the square are length 9.

We could plug each of the candidate points into the distance formula.

Or we could observe that the vertex will be on a circle having equation *x* – 5)^{2} + (*y* + 4)^{2} = 81

Either way, after some computational hassle, we see that (c) works: (2, 6√2 – 4).