Quandaries
and Queries 

Find the shortest distance from the point (15, 2.5) to the line 5x+6y=30. The problem I am having is substituting the point into the perpendicular line. I'm not sure how to do it. I really need this answer soon! Please respond as soon as you can. Thanks. carly. 

Hi Carly,
The line 5x + 6y = 30 can be rewritten
So its slope is ^{5}/_{6} and hence a line perpendicular to it has slope ^{6}/_{5}. Hence the line through (15, 2.5) and perpendicular to the line you were given is
(I use the pointslope form for the equation of the line but you may use another form.) Simplify the equation and solve the two equations to find the point Q on the diagram. The distance you want is the distance from P to Q. Penny 

