Question

On a coordinate graph, your house is located at the origin (0,0) You leave your house and walk 6 blocks north. Then you turn and walk 22 blocks west. Since it is getting late, you decide to walk straight back home. How many blocks is it to walk straight back to your house? Round your answer to the nearest tenth​

Answer 1

22.8 blocks

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:

`a^2+b^2=c^2`

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:

`a^2+b^2=c^2\\c=√(a^2+b^2)`

Now, plug in the side lengths of the triangle:

`c=√(6^2+22^2)`

Now simplify!

`c=√(36+484) \\x=√(520) x=22.8`

It is 22.8 blocks back to your house! Hope this helps!