Pipeline Path and Town Radius: Do I Need to Reroute? | Explanation Included

[ireallyneedhelp]

I need help with this simple question!

Can some please explain to me on how to solve this problem?

A pipeline follows a path given by y=2x + 20. A town is centered at
T(50,0) and has a radius of 5km. By state law pipelines must be 50 km's away from towns. Does this pipe need to be rerouted? Explain.


Please I really need help wiht this question! Thanks

 

[Hurkyl]

This should probably be in the homework help section.

Anyways, can you show us what you've gotten on your own?

 

[STAii]

I will give you a little push.
First of all, you might find a redy-to-use equation to find the distance between a point and line in some book, if you don't here is what you can do.
The distance between a point and a line (call it line1) is the length of a line (call it line2) vertical on line1 and with one side on line1 and the other side on the point (try to draw it to understand what i mean)
First of all, find the slope of the pipeline (line1).
Now, if we find the slope of line2, we would be able to find the equation that represents line2 (you know how to find a line equation knowning its slope and a point that it goes through ?).
To find the slope of line2, remember that it is vertical on line1, and therefore m₁*m₂=-1 (where m₁ is the slope of line1, m₂ is the slope of line2).
Now that you have the equation of line2, you can find the point at which line1 and line2 cross each other (just solve both equations for the unknown x and y).
Now use phytagorean theory to find the distance between the target point, and the point of crossing between line1 and line2.