Answer:
22.8 blocks
Step-by-step explanation:
We can think of your path as traveling on a coordinate plane. You start by walking 6 units in the positive y direction, then 22 units in the negative x direction, then walking from this point (-22, 6) back to (0, 0)
This path draws a right triangle. The shorter leg is 6 units long, and the longer end is 22 units long. You want to find the hypotenuse of this triangle.
The hypotenuse is found using the Pythagorean theorem:
[tex]a^2+b^2=c^2[/tex]
A and B represent the sides of the triangle, and c represents the hypotenuse!
Before plugging in the functions, isolate c, since that's the answer we're looking for:
[tex]a^2+b^2=c^2\\c=\sqrt{a^2+b^2}[/tex]
Now, plug in the side lengths of the triangle:
[tex]c=\sqrt{6^2+22^2}[/tex]
Now simplify!
[tex]c=\sqrt{36+484} \\x=\sqrt{520} x=22.8[/tex]
It is 22.8 blocks back to your house! Hope this helps!
