Pipeline is laid underwater fro a offshore drilling platform (210,57) to the closest point on shore. The shore is a straight line, and joins the refinery at (150,305) to the harbour at (215,-20). Find the distance the oil will flow from the offshore platform to the shore.

The line equation that represents

the distance between the harbor

and the refinery is

5x+y-1055=0

We need the shortest distance from this line to the point (210,57) at the oil platform.

Use the distance from a point to a line formula:

d=\frac{|Ax_{0}+By_{0}+C|}{\sqrt{A^{2}+B^{2}}}

Wherex_{0}=210, \;\ y_{0}=57.

A, B, C are the coefficients in the line equation. Where the line equation has standard form

Ax+By+C=0

plug and chug.

So what's the distance the oil will flow from the platform to the shore?

You're welcome.

Use the formula I gave you. I done everything else, all you have to do is enter the given values.