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 88 miles due north of the warehouse.
Coordinate grid shown from negative 66 to positive 66 on x axis at intervals of 11 and negative 66 to positive 66 on y axis at intervals of 11. A straight line is shown between the points labeled Airport and Warehouse. Airport is the ordered pair negative 33, 44, and Warehouse is the ordered pair 33 and negative 44. 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? (5 points)
176 miles
198 miles
220 miles
250 miles
To find the total number of miles the truck traveled, we need to calculate the distance between the warehouse and the airport, and then add the distance between the airport and the factory.
The distance between two points on a coordinate plane can be found using the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
For the distance between the warehouse and the airport, the coordinates are:
Warehouse: (33, -44)
Airport: (-33, 44)
Solving for the distance:
d1 = sqrt((-33 - 33)^2 + (44 - (-44))^2)
d1 = sqrt((-66)^2 + (88)^2)
d1 = sqrt(4356 + 7744)
d1 = sqrt(12100)
d1 = 110
So, the distance between the warehouse and the airport is 110 miles.
For the distance between the airport and the factory, the coordinates are:
Airport: (-33, 44)
Factory: (-33, 132)
Solving for the distance:
d2 = sqrt((-33 - (-33))^2 + (132 - 44)^2)
d2 = sqrt(0^2 + 88^2)
d2 = sqrt(7744)
d2 = 88
So, the distance between the airport and the factory is 88 miles.
Finally, we can calculate the total number of miles the truck traveled:
Total distance = distance from the warehouse to the airport + distance from the airport to the factory
Total distance = 110 + 88
Total distance = 198 miles
Therefore, the truck traveled a total of 198 miles.