Suppose your home is located at (0, 0) on a coordinate plane. The school is located 2 miles south of your home. The mall is located 5 miles west of the school. What is the shortest distance, in miles, between your home and the mall? Round to the nearest hundredth.
To find the shortest distance between your home and the mall, we need to find the distance between your home and the school, then between the school and the mall, and finally combine these distances.
First, let's find the distance between your home and the school. Since the school is 2 miles south of your home, the distance is simply 2 miles.
Next, let's find the distance between the school and the mall. Since the mall is 5 miles west of the school, we can create a right triangle with the legs being 5 miles and 2 miles (the distance between your home and the school). We can use the Pythagorean theorem to find the hypotenuse (the distance between the school and the mall).
The distance between the school and the mall is √(5^2 + 2^2) = √29 ≈ 5.39 miles
Finally, we can calculate the total shortest distance between your home and the mall by adding the two distances we found:
2 miles + 5.39 miles ≈ 7.39 miles
Therefore, the shortest distance between your home and the mall is approximately 7.39 miles.