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

Guest Jul 24, 2022

#1**0 **

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

katelynsknee Jul 25, 2022