SOLUTION: Please help me solve this When a train carying poisonous gas derails, authorities order all people living within 5 miles to evacuate the area. The derailment has coordinates (

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Question 388688: Please help me solve this

When a train carying poisonous gas derails, authorities order all people living within 5 miles to evacuate the area. The derailment has coordinates (-5,-5) and your location is at (4,1). How far are you from the derailment? Round your answer to two decimal places (coordinates are in miles).












Found 2 solutions by jim_thompson5910, jsmallt9:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
We basically want to find the distance between the two points.




Note: is the first point . So this means that and .
Also, is the second point . So this means that and .


Start with the distance formula.


Plug in , , , and .


Subtract from to get .


Subtract from to get .


Square to get .


Square to get .


Add to to get .


Simplify the square root.


So our answer is


Which approximates to


So the distance is approximately 10.817 miles.



If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
Another way to ask the same question is: "What is the distance between (-5, -5) and (4, 1)?" Phrased this way we should be able to figure out that this is a job for the distance formula:

Inserting the coordinates we have been given we get:

which simplifies as follows:



This is the exact distance. I will leave it up to you and your calculator to find this square root and round off the answer to two decimal places.
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