A. Our diagram have six location: my house (2,1), a movie theater (5,3), the school (6,6), the police station (3,-2), the airport (-3,3), and the mall (-2,-3)
B. Distance between my house and the movie theater:
To calculate the distance we are going to use the points (2,1) and (5,3) to create a right triangle with tow legs of measures 3 and 2; the hypotenuse of the right triangle will be the distance between my house and the movie theater.
Using the Pythagorean theorem:
![d^2=3^2+2^2](https://tex.z-dn.net/?f=d%5E2%3D3%5E2%2B2%5E2)
![d^2=9+4](https://tex.z-dn.net/?f=d%5E2%3D9%2B4)
![d^2=13](https://tex.z-dn.net/?f=d%5E2%3D13)
![d= \sqrt{13}](https://tex.z-dn.net/?f=d%3D%20%5Csqrt%7B13%7D%20)
We can conclude that the distance between my house and the movie theater is
![\sqrt{13}](https://tex.z-dn.net/?f=%20%5Csqrt%7B13%7D%20)
Our second distance is the distance between the police station and the airport:
This time we are using the points (3,-2) and (-3,3) to create a right triangle with legs of measures 6 and 5; the hypotenuse of our triangle will be the the distance between our points:
![d^2=6^2+5^2](https://tex.z-dn.net/?f=d%5E2%3D6%5E2%2B5%5E2)
![d^2=36+25](https://tex.z-dn.net/?f=d%5E2%3D36%2B25)
![d^2=61](https://tex.z-dn.net/?f=d%5E2%3D61)
![d= \sqrt{61}](https://tex.z-dn.net/?f=d%3D%20%5Csqrt%7B61%7D%20)
We can conclude that the distance between the police station and the airport is
C. Distance form the park to the Fire Station:
![d^2=3^2+1^2](https://tex.z-dn.net/?f=d%5E2%3D3%5E2%2B1%5E2)
![d^2=9+1](https://tex.z-dn.net/?f=d%5E2%3D9%2B1)
![d^2=10](https://tex.z-dn.net/?f=d%5E2%3D10)
![d= \sqrt{10}](https://tex.z-dn.net/?f=d%3D%20%5Csqrt%7B10%7D%20)
We can conclude that the distance from the park to the Fire Station is
![\sqrt{10}](https://tex.z-dn.net/?f=%20%5Csqrt%7B10%7D%20)
Distance from the stadium to the mall:
![d^2=2^2+1^2](https://tex.z-dn.net/?f=d%5E2%3D2%5E2%2B1%5E2)
![d^2=4+1](https://tex.z-dn.net/?f=d%5E2%3D4%2B1)
![d^2=5](https://tex.z-dn.net/?f=d%5E2%3D5)
![d= \sqrt{5}](https://tex.z-dn.net/?f=d%3D%20%5Csqrt%7B5%7D%20)
We can conclude that the distance from the stadium to the mall is
D. What is the distance between your house and the mall?
Answer:
![d^2=4^2+4^2](https://tex.z-dn.net/?f=d%5E2%3D4%5E2%2B4%5E2)
![d^2=16+16](https://tex.z-dn.net/?f=d%5E2%3D16%2B16)
![d^2=32](https://tex.z-dn.net/?f=d%5E2%3D32)
![d= \sqrt{32}](https://tex.z-dn.net/?f=d%3D%20%5Csqrt%7B32%7D%20)
![d=4 \sqrt{2}](https://tex.z-dn.net/?f=d%3D4%20%5Csqrt%7B2%7D%20)
We can conclude that the distance between my house and the mall is
![4 \sqrt{2}](https://tex.z-dn.net/?f=4%20%5Csqrt%7B2%7D%20)
What is the distance between the movie theater and the school?
answer:
![d^2=3^2+1^2](https://tex.z-dn.net/?f=d%5E2%3D3%5E2%2B1%5E2)
![d^2=9+1](https://tex.z-dn.net/?f=d%5E2%3D9%2B1)
![d^2=10](https://tex.z-dn.net/?f=d%5E2%3D10)
![d= \sqrt{10}](https://tex.z-dn.net/?f=d%3D%20%5Csqrt%7B10%7D%20)
We can conclude that the distance between the movie theater and the school is