Expert: Richard J. Raridon - 9/3/2008

Question
What is the shortest distance between the point (5,2) and the line y=2x+3?  Also, find the coordinates of the midpoint of the line segment.

Answer
First you have to find the equation of the line perpendicular to
y=2x+3 and going through (5,2).  That line is x+2y=9.  Then you find the intersection of the two lines which is (3/5,21/5).  So the distance between (3/5,21/5) and (5,2) is 4.92.
The midpoint is (14/5,31/10)