Final answer:
If Stephanie had driven directly from her house to her mother's house, she would have driven approximately 12.2 miles, based on the Pythagorean theorem applied to the 10 miles north and 7 miles east she traveled.
Step-by-step explanation:
To determine the direct distance Stephanie would have driven from her house to her mother's house, we can visualize her path as two sides of a right-angle triangle, where driving 10 miles north and then 7 miles east represents the two legs of the triangle. This triangle's hypotenuse is the straight-line distance we're trying to find.
The Pythagorean theorem states that in a right-angle triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This can be expressed as c² = a² + b².
In Stephanie's case:
- Northward distance (a) = 10 miles
- Eastward distance (b) = 7 miles
Using the Pythagorean theorem:
c² = (10 miles)² + (7 miles)²
c² = 100 + 49
c² = 149
c = √149 miles
When we calculate the square root of 149, we find that c, the straight-line distance, is approximately 12.2 miles. We would round this to the nearest tenth, which is 12.2 miles as well.
Therefore, the correct answer is none of the provided options as they don't include 12.2 miles. Stephanie would have driven approximately 12.2 miles directly to her mother's house.