The points (-1,4) and (2,-8) are adjacent vertices of a square. What is the area of the square?
+9 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
