Final answer:
By calculating the distances using the coordinates provided for the school, mall, and library, it is determined that Mike traveled 46 units, whereas Henry traveled 30 units. The difference is 16 units, which is the number of additional miles Mike traveled.
Step-by-step explanation:
The student's question involves calculating the difference in distances traveled from the school to the library via the mall, as compared to traveling directly from the school to the library. To solve this, we will use the coordinates provided to find the length of the paths that Mike and Henry took.
Mike traveled from the school (15, -10) to the mall (15, 6) and then from the mall to the library (-15, 6). The vertical distance from the school to the mall is the difference in the y-coordinates, which is 16 units. The horizontal distance from the mall to the library is the difference in the x-coordinates, which is 30 units. Thus, Mike traveled a total of 16 + 30 = 46 units.
Henry traveled directly from the school to the library, which forms the third side of the triangle. Since the library and the mall have the same y-coordinate, and Henry's trip is a direct horizontal line, the distance is the same as Mike's horizontal distance: 30 units.
Hence, Mike traveled 46 units while Henry traveled 30 units. The difference is 46 - 30 = 16 units, which is the number of additional miles Mike traveled compared to Henry.