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) About Me  (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 x%5B1%5D=-5 and y%5B1%5D=-5.
Also, is the second point . So this means that x%5B2%5D=4 and y%5B2%5D=1.


d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 Start with the distance formula.


d=sqrt%28%28-5-4%29%5E2%2B%28-5-1%29%5E2%29 Plug in x%5B1%5D=-5, x%5B2%5D=4, y%5B1%5D=-5, and y%5B2%5D=1.


d=sqrt%28%28-9%29%5E2%2B%28-5-1%29%5E2%29 Subtract 4 from -5 to get -9.


d=sqrt%28%28-9%29%5E2%2B%28-6%29%5E2%29 Subtract 1 from -5 to get -6.


d=sqrt%2881%2B%28-6%29%5E2%29 Square -9 to get 81.


d=sqrt%2881%2B36%29 Square -6 to get 36.


d=sqrt%28117%29 Add 81 to 36 to get 117.


d=3%2Asqrt%2813%29 Simplify the square root.


So our answer is d=3%2Asqrt%2813%29


Which approximates to d=10.817


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(3759) About Me  (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:
d+=+sqrt%28%28x%5B2%5D+-+x%5B1%5D%29%5E2+%2B+%28y%5B2%5D+-+y%5B1%5D%29%5E2%29
Inserting the coordinates we have been given we get:
d+=+sqrt%28%284+-+%28-5%29%29%5E2+%2B+%281+-+%28-5%29%29%5E2%29
which simplifies as follows:
d+=+sqrt%28%289%29%5E2+%2B+%286%29%5E2%29
d+=+sqrt%2881+%2B+36%29
d+=+sqrt%28117%29
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.