Question

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?
a) 176 miles
b) 198 miles
c) 220 miles
d) 250 miles

Answer 1

The total number of miles the truck traveled is 198 miles.

Step-by-step explanation:

To find the total number of miles the truck traveled, we need to find the distances between the warehouse and the airport, and between the airport and the factory, and then add them up. From the coordinate grid, we can see that the warehouse is at (33, -44) and the airport is at (-33, 44). The distance formula between two points (x1, y1) and (x2, y2) is given by:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we can calculate the distances as follows:

distance between warehouse and airport = sqrt((-33 - 33)^2 + (44 - (-44))^2) = sqrt((-66)^2 + (88)^2) = sqrt(4356 + 7744) = sqrt(12100) = 110 miles

distance between airport and factory = 88 miles (given)

Therefore, the total number of miles the truck traveled is 110 miles + 88 miles = 198 miles.

Answer 2

To calculate the total distance the truck travels, we find the distance between the airport and the warehouse using the Pythagorean theorem, which is 110 miles. We then add the distance to the factory, which is 88 miles due north of the warehouse, making the total distance 198 miles.Therefore, the correct answer is option (b) 198 miles.

Step-by-step explanation:

The question requires calculating the total distance a truck travels on a coordinate grid.

The truck goes from the warehouse to the airport and then to the factory, which is 88 miles due north of the warehouse.

We calculate the first leg of the journey, which is the distance between the warehouse and the airport.

Then we add the northward journey from the warehouse to the factory.

To find the distance between the airport and the warehouse, we use the coordinates given for both places (Airport at (-33, 44) and Warehouse at (33, -44)) and apply the Pythagorean theorem.

The distance between two points on a coordinate grid is the square root of the sum of the squares of the difference in x-values and the difference in y-values. This gives us:

Distance between Airport and Warehouse = √[(33 - (-33))^2 + (44 - (-44))^2] = √[66^2 + 88^2] = √[4356 + 7744] = √[12100] = 110 miles.

The second leg of the journey is simply moving 88 miles north from the warehouse to the factory, which is already given in the question.

Hence, the total distance the truck traveled is 110 miles (from the warehouse to the airport) plus 88 miles (from the warehouse to the factory) which equals 198 miles.

Therefore, the correct answer is option (b) 198 miles.