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

• dubious9
In summary, the conversation involves the request for help in finding the distance between two points, P and Q, given their coordinates and the use of the distance formula. The importance of working through the problem rather than relying on external resources is emphasized.
dubious9

## Homework Statement

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

## Homework Equations

distance formula

d(P,Q) = √(x1-x2)2+(y1-y2)2

## 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?

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dubious9 said:

## Homework Statement

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

## Homework Equations

distance formula

d(P,Q) = √(x1-x2)2+(y1-y2)2

## 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?

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.

dubious9 said:

## Homework Statement

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

## Homework Equations

distance formula

d(P,Q) = √(x1-x2)2+(y1-y2)2

## 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?

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

Mark44 said:
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.

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.

dubious9 said:
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)
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.
dubious9 said:
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.
You will learn more by working the problem than by looking at someone else's work.

dubious9 said:
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.

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.

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.

dubious9 said:
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.

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.

dubious9 said:
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.
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.
dubious9 said:
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.
We're saying that working the problem is a much better way of learning than any of the routes you want to pursue.

## 1. What is the distance formula?

The distance formula is a mathematical equation used to calculate the distance between two points on a graph. It is often represented as d = √(x2-x1)^2 + (y2-y1)^2, where (x1, y1) and (x2, y2) are the coordinates of the two points.

## 2. How do you use the distance formula?

To use the distance formula, you need to plug in the coordinates of the two points into the equation. Make sure to label which point is (x1, y1) and which point is (x2, y2) to avoid confusion. Then, you can simplify the equation and solve for the distance, d.

## 3. What is the significance of the unknowns in the given distance formula?

In the given distance formula with unknowns (13x,-23x) (6x,x) x>0, the unknown variables represent the x and y coordinates of the two points. The variable x>0 indicates that the value of x for both points must be positive, which is a common restriction in distance formula problems.

## 4. Can the distance formula be used for any two points on a graph?

Yes, the distance formula can be used for any two points on a graph as long as you know their coordinates. It is a universal equation that applies to all types of graphs, including linear, quadratic, and circular graphs.

## 5. How does the distance formula relate to real-life situations?

The distance formula is often used in real-life situations to calculate the distance between two locations or objects. For example, it can be used to determine the distance between two cities on a map or the length of a diagonal path between two buildings. It is also commonly used in physics and engineering to calculate the distance between two moving objects.

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