Minimum distance between two parallel lines - Part II

This post continues my previous one, where we set up our problem and I gave you a few tips that may have been enough to set you off in the correct direction. In this post, I'll outline the strategy we'll use to solve the question, and then we will tackle the numbers.

So, for now, we HAVE the following information:

• First line: y=(5/2)x - 4
• Point on second line = (3,8)
• Two parallel lines.... slopes are the same
• Shortest distance between the line and point will be perpendicular to the lines. Recall: the slope that is perpendicular to slope m is -1/m.

Think about our strategy backwards first. What do we NEED to solve this?

• The distance can be calculated by the distance formula. What does this need?
• We need 2 points! . We have one, and now we need the second point, which will lie on our first line. How do we find this point?
• We find this point where this line INTERSECTS a perpendicular line that passes through the given point. This is because the perpendicular line will be the shortest distance between our two parallel lines. So, how do we find this intersection?
• The intersection occurs where the two lines meet. More precisely, the intersection is where the equations of the two lines are equal. We have the first equation. How do we get the second equation?
• The second equation comes from the given point, and the slope perpendicular to our parallel lines.

It seems like a lot, but if you follow it through, you can see the logic behind all of the steps. Find one thing which leads to another, which leads to another, which leads us to the solution.

This is another good piece of advise for working with more complex problems. Look at what you! need to find, and try to step backwards, as I did above. Ask! yoursel f "what do I need to find this?" and then "what do I need to find that?" and you will then find that you have outlined your own strategy of how to solve the problem!

So, now that we have our strategy, let's get to it. Move ahead to my next post where we'll throw the numbers into play, and go for our answer. :)

How to do Distance Formula