First Chapter of Text: distance formula with unknowns (13x,-23x) (6x,x) x>0

dubious9

1. The problem statement, all variables and given/known data
Find the distance between P and Q

P(13x,-23x), Q(6x,6), x>0

*This came from Chapter 1 Linear Functions, Equations, and inequalities Section 1.1 Real Numbers and the Rectangular coordinate System of A Graphical Approach to Precalculus with Limits by Hornsby et al


2. Relevant equations

distance formula

d(P,Q) = √(x₁-x₂)²+(y₁-y₂)²

3. The attempt at a solution

I mostly need to what this so I can put a query into google. It looks like something to do with the equations of the lines of the triangle like line P is (mx,bx) and line Q is (mx,bx) but I really have no idea...graphical transformations or something?

Mark44

Instead of googling this, why don't you just work the problem? You have the two points, and you have the formula for the distance between two points. Substitute the given points into your formula.

symbolipoint

Google is not needed. You have the coordinates and you know/have the distance formula.

dubious9

Hello,

The reason I don't want to work the problem is because not much is mentioned about the problem in my text because it is precalculus and not remedial algebra.

When I 'google' something I'm trying to find articles or explinations containing details such as:

P(13x, -23x), Q(6x,x)

Where instead of just plugging some numbers like 12, -23 and 6,1 I have some variables in with my coordinates...I am starting to think this is a simplification problem...nothing to do with changing the locations of points...after all it is the first section of my precalculus text.

I think I am going to get the student solutions manual for this text. A book that will work out the problems for me and turn a light on when I want to google things.

Thanks.

Mark44

What you describe is not a good approach. A better way to do things is to just try them out. The coordinates of point P are 13x and -23x. The coordinates of Q are 6x and x.

You have the distance formula. Just plug the coordinates of the points into this formula to get the distance. After this, simplify the result as much as possible.

You should not be wasting your time trying to find something by a web search.
You will learn more by working the problem than by looking at someone else's work.

Ray Vickson

What you are describing is just about the WORST way to learn; it will prepare you for nothing and will not help you on exams, etc. No: the useful way to do it is to just sit down and write out the details. You have the coordinates of the points and you have the distance formula, so use them. This applies whether the course is pre-calc, remedial algebra or anything else.

dubious9

It appears as though there are people here with more important precalculus homework problems and I should take my question to a remidial algebra forum somewhere else on the internet. Mark44 and Ray Vickson, instead of telling me to 'just work the problem' why don't you 'just' tell me my question is innappropriate. Just because I am looking for hits on google, instructor solutions, or talking to you on the internet doesn't mean I'm in a hurry.

Ray Vickson

Several people have given you the best possible advice for helping you learn the material. Everybody who has responded to you are current or former instructors with years of experience, so ignore their advice at your peril. Good luck.

Mark44

That's not at all what we've said, nor is it what we mean. What we both did say is that you have the points and you have the formula, so just substitute the coordinates of the points in the distance formula. I think this is the third time I've said this, and Ray said it at least once.

Here at Physics Forums, we operate under the philosophy that students learn best by doing the bulk of the work themselves, NOT by seeing the answers.
We're saying that working the problem is a much better way of learning than any of the routes you want to pursue.