ExplanationSince the point (2, 2) is a vertex of square S and the point (6, 6) is the midpoint of the diagonals, it follows that the point (10, 10) is also a vertex of the square. Using this information you can sketch square S in the xy-plane, labeling the points (2, 2), (6, 6), and (10, 10) as shown in the figure below.

From the figure, you can see that S has sides of length 8. Therefore the area of S is \(8^2\) = 64. Hence Quantity A is equal to Quantity B, and the correct answer is Choice C.

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