While hiking along the pacific coast trail, you become lost in the woods. rather than panic, you pull out your trail map to try and find the shortest way out. on the map you see a straight road and on the road are some coordinates. at one end of the road are the coordinates (150, 145) and at the other end the coordinates are (550,375). the gps on your phone tells you that your current location is at (220,430) all the coordinates are in miles. use this information to calculate the shortest distance to the road. this is like a project ill give brainliest

There are many ways to write the equation of the line representing the road. Under the circumstances, it may work well to use this form.
  ∆y·(x -x1) - ∆x·(y -y1) = 0
where ∆x = x2 -x1, and ∆y = y2 -y1.

Substituting the given numbers, this is
  (375-145)(x -150) -(550-150)(y -145) = 0
  230(x -150) -400(y -145) = 0
Dividing by 10 and eliminating parentheses, this becomes
  23x -40y +2350 = 0

This general-form equation is very useful for finding the distance from a point to a line. For general form line ax+by+c=0, the distance to the line from point (x,y) is ...
  d = |ax +by +c|/√(a²+b²)

Using this formula and the given point, the shortest distance to the road is ...
  d = |23×220 -40×430 +2350|√(23²+40²)
  d = 9790/√2129
  d ≈ 212.175

The shortest distance from your location to the road is about 212.2 miles.

_____
A geometry program comes to the same conclusion.

Hello!

the answer is:

the correct option is the option b.

why?

to calculate the surface area of the right cylinder, we need to use the following formula:

from the picture we know that:

so, substituting and calculting we have:

hence, we have that the correct option is the option b.

have a nice day!