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# help coordinates

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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