The map shows the location of the airport and a warehouse in a city. Though not displayed on the map, there is also a factory 112 miles due north of the warehouse. Coordinate grid shown from negative 84 to positive 84 on x axis at intervals of 14 and negative 84 to positive 84 on y axis at intervals of 14. A straight line is shown between points labeled Airport and Warehouse. Airport is the ordered pair negative 42, 56, and Warehouse is the ordered pair 42 and negative 56. A signage showing directions North, South, East, and West is shown in the empty quadrant on the graph. A truck traveled from the warehouse to the airport and then to the factory. What is the total number of miles the truck traveled? 112 154 224 252
Accepted Solution
A:
224 miles
OK. The total distance traveled is the sum of two smaller trips. Let's calculate their distances independently.
Warehouse to Airport
(42, -56) to (-42, 56)
Using the Pythagorean theorem
d = sqrt((42 - -42)^2 + (-56 - 56)^2)
d = sqrt(84^2 + (-112)^2)
d = sqrt(7056 + 12544)
d = sqrt(19600)
d = 140
Airport to Factory
(-42, 56) to (42, -56+112)
(-42, 56) to (42, 56)
Using the Pythagorean theorem again.
d = sqrt((-42 - 42)^2 + (56 - 56)^2)
d = sqrt((-84)^2 + 0^2)
d = sqrt(7056 + 0)
d = sqrt(7056)
d = 84
So the truck traveled 140 + 84 = 224 miles.