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matt1595 · Oct 25, 2010, 09:16 AM

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.

galactus · Oct 25, 2010, 01:23 PM

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:

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

Where $x_{0}=210, \;\ y_{0}=57$ .

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

$Ax+By+C=0$

plug and chug.

matt1595 · Oct 25, 2010, 01:47 PM

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

galactus · Oct 25, 2010, 01:59 PM

You're welcome.

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