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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 19, 2021
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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?

 

Hello wizzymath!

 

\(A=(\dfrac{d}{\sqrt{2}})^2=\dfrac{d^2}{2}\)

\(d^2=(x_2-x_1)^2+(y_2-y_1)^2\\ d^2=(7-1)^2+(4-2)^2\\ d^2=40\)

\(A=\dfrac{d^2}{2}=\dfrac{40}{2}\)

\(A=20\)

 

The area of the square is 20.

laugh  !
 

 Feb 19, 2021

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