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The points (-1,4) and (2,-8) are adjacent vertices of a square. What is the area of the square?

 Jul 24, 2022
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The adjacent verticies of a square split the square into two congruent triangles.

 

Using the distance formula:

 

\(\sqrt{(2-(-1))^2 +(-8-4)^2}\)

 

We can conclude that the Hypotenuse of the two congruent triangles is \(\sqrt{153}\)

 

Now using the Pythagorean Theorem we can find the side lengths of the square. Since the length and width of a square are equal we can write the following equation:

 

\({a}^{2}+{a}^{2}=\sqrt{153}^2\)

 

--> 153=2a^2

--> 76.5=a^2

--> a= sqrt(76.5)

 

To find the area of the square we just do length times width and get that the area of said square is 76.5 units!!!!!!

 

-knee

 Jul 25, 2022

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