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 72 miles due north of the warehouse.
A truck traveled from the warehouse to the airport and then to the factory. What is the total number of miles the truck traveled?


54 miles
72 miles
144 miles
162 miles

Answer 1

Answer:

C. 144 miles

Step-by-step explanation:

We have that the truck traveled from the warehouse to the airport and then to factory.

First we will find the distance between the warehouse and the airport using the 'Distance formula'.

'Distance Formula' gives the distance between two points $(x_{1},y_{1})$ and  $(x_{2},y_{2})$ by $\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$.

As, from the graph, we have,

Warehouse is located at (27,-36) and Airport is located at (-27,36).

So, the distance between them is,

$\sqrt{(-27-27)^{2}+(36-(-36))^{2}}$

i.e. $\sqrt{(-27-27)^{2}+(36+36)^{2}}$

i.e. $\sqrt{(-54)^{2}+(72)^{2}}$

i.e. $\sqrt{2916+5814}$

i.e. $\sqrt{8100}$

i.e. $90$

So, the distance from warehouse to the airport is 90 miles.

Moreover, as the truck further traveled to the factory which is 72 miles north of the warehouse.

So, the factory is located at (27,72-36) i.e. (27,36).

Then, the distance from the airport (-27,36) to the factory is (27,36) is,

$\sqrt{(27+27)^{2}+(36-36)^{2}}$

$\sqrt{54^{2}+0^{2}}$

$\sqrt{2916}$

$54$

So, the distance from airport to the factory is 54 miles.

Thus, the total distance traveled by the truck is 90 + 54 = 144 miles.

Hence, option C is correct.

Answer 2

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\sqrt{(-27-27)^2+(36+36)^2}\\\\ \sqrt{54^2+72^2} \\\\ \sqrt{8100} \\\\90\\\\\\90+54 =\boxed { 144}\\\\\sf The~ distance~ 90~ is~ from ~the~ warehouse~ to ~the ~airport\\\\The~ distance~ 54~ is~ from ~the~ airport~ to ~the~ factory\\\\So,~ the~ total~ distance~ is~ 144$