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On a Cartesian coordinate plane, points (1,2) and (7,-4) are opposite vertices of a square. What is the area of the square?

Feb 23, 2021

The distance between $(1,2)$ and $(7,-4)$ is $\sqrt{6^2+6^2}=6\sqrt{2}$ by the distance formula. This is the length of the diagonal of the square. Recall that the diagonal is equal to $\sqrt{2}\cdot\text{side length}$. Therefore, $\text{side length}=6$, and $\text{Area}=6^2=\boxed{36}$.