If the vertices B and D of a square ABCD are (2,3) and (4,1) respectively, then what is the area of the square?

Explanation

The distance between the opposite vertices B(2,3) and D(4,1) gives the length of the diagonal d. Using the distance formula, d = \sqrt{(4-2)^2 + (1-3)^2} = \sqrt{4+4} = \sqrt{8}. The area of a square relates to its diagonal by \frac{1}{2}d^2. Thus, the area is \frac{1}{2}(8) = 4 square units.

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