The map shows the location of a mall, library, and school in a city:
Coordinate grid shown from negative 16 to positive 16 on x axis at intervals of 2, and negative 10 to positive 10 on y axis at intervals of 2. A triangle is shown with vertices labeled Library, Mall, and School. Library is the ordered pair negative 15, 6, Mall is the ordered pair 15, 6, and School is the ordered pair 15 and negative 10.
Mike traveled from the school to the mall and then from the mall to the library. Henry traveled from the school to the library. How many more miles did Mike travel than Henry? (1 point)
10 miles
12 miles
34 miles
46 miles
To find the distance between two points on a coordinate grid, we can use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
For Mike:
x1 = 15, y1 = -10 (school)
x2 = 15, y2 = 6 (mall)
d1 = √((15 - 15)^2 + (6 - (-10))^2)
= √(0 + 256)
= √256
= 16
For Henry:
x1 = 15, y1 = -10 (school)
x2 = -15, y2 = 6 (library)
d2 = √((-15 - 15)^2 + (6 - (-10))^2)
= √((-30)^2 + (16)^2)
= √(900 + 256)
= √1156
= 34
Therefore, Mike traveled 16 miles and Henry traveled 34 miles. The difference is 34 - 16 = 18 miles.
Therefore, the correct answer is that Mike traveled 18 miles more than Henry.