Question

rachel started at point x and rode her bicycle 12 miles south to point y. from point y, rachel rode her bicycle 5 miles east to point z. what is the distance from point x to point z? distance from point x to point z ____ miles

Explanation:

Step1: Identify right - triangle and apply Pythagorean theorem

The path from X to Y (12 miles), Y to Z (5 miles), and X to Z forms a right - triangle. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $a = 12$, $b = 5$, and $c$ is the distance from X to Z.

Step2: Substitute values into the formula

Substitute $a = 12$ and $b = 5$ into $a^{2}+b^{2}=c^{2}$. We get $12^{2}+5^{2}=c^{2}$, which is $144 + 25=c^{2}$, so $c^{2}=169$.

Step3: Solve for $c$

Take the square root of both sides. Since $c>0$, $c=\sqrt{169}=13$.

Answer:

13