Determine the equation

[Ana.stasia]

The question is
Determine the equation of the line that is parallel to the lines 3x-2y-1 = 0 and 3x-2y-13 = 0 and is equally distant from both lines.

I have written the formula we are supposed to use along the way.

I also know everything so far I did is correct. But what do I do now, with only p???

 

[lev888]

The question is
Determine the equation of the line that is parallel to the lines 3x-2y-1 = 0 and 3x-2y-13 = 0 and is equally distant from both lines.

I have written the formula we are supposed to use along the way.

I also know everything so far I did is correct. But what do I do now, with only p???

View attachment 25055

Looks complicated. Do you have to use that formula?
I don't understand how you got the expressions for p1 and p2.

If you are free to use any method, here's what I would do:
1. Convert the 2 equations into slope/intercept form.
2. The slopes of parallel lines are the same - this gives you the slope
3. The y-intercept you need is midway between the other 2 intercepts (you may need to prove it, not too difficult).

 

[Ana.stasia]

Looks complicated. Do you have to use that formula?
I don't understand how you got the expressions for p1 and p2.

If you are free to use any method, here's what I would do:
1. Convert the 2 equations into slope/intercept form.
2. The slopes of parallel lines are the same - this gives you the slope
3. The y-intercept you need is midway between the other 2 intercepts (you may need to prove it, not too difficult).

I do know of that way, however, the result states to use p=7/sqrt 13

 

[JeffM]

I hate formulas. The formula that you are supposed to use is for what purpose? Where did you get the angle you are using? What is the definition of p?

 

[Ana.stasia]

I hate formulas. The formula that you are supposed to use is for what purpose? Where did you get the angle you are using? What is the definition of p?

To determine an equation. I need the angle for the formula. I didn't get it. I am asking for an advice on how to get it. P is the distance from (0,0) to another point.

 

[JeffM]

In equation 1, if y = 0, x = 1/3, and the angle is 0. If x = 0, y = -1/2 and the angle is - pi/2 radians.

[MATH]\dfrac{1}{3} * cos(0) + 0 * sin(0) - p = 0 \implies \dfrac{1}{3} - p = 0 \implies p = \dfrac{1}{3}.[/MATH]
And (1/3, 0) is clearly distant from the origin by 1/3

[MATH]0 * cos (- \pi/2) - \dfrac{1}{2} * sin(- \pi /2) - p = 0 \implies - \dfrac{1}{2} * (-1) - p \implies p = 1/2.[/MATH]
And (0, -1/2) is clearly distant from the origin by 1/2.

Where did these square roots of 13 even come from? And why?

Can you do the problem now?

 

[Ana.stasia]

In equation 1, if y = 0, x = 1/3, and the angle is 0. If x = 0, y = -1/2 and the angle is - pi/2 radians.

[MATH]\dfrac{1}{3} * cos(0) + 0 * sin(0) - p = 0 \implies \dfrac{1}{3} - p = 0 \implies p = \dfrac{1}{3}.[/MATH]
And (1/3, 0) is clearly distant from the origin by 1/3

[MATH]0 * cos (- \pi/2) - \dfrac{1}{2} * sin(- \pi /2) - p = 0 \implies - \dfrac{1}{2} * (-1) - p \implies p = 1/2.[/MATH]
And (0, -1/2) is clearly distant from the origin by 1/2.

Where did these square roots of 13 even come from? And why?

Can you do the problem now?

It come from sqrt 4+9, that's a formula. As I said, everything I did so far is correct 100% as I have this part explained in the solution.

 

[JeffM]

Why don’t you give us what you know from the solution? Why make us guess what is going on?

 

[Dr.Peterson]

Determine the equation of the line that is parallel to the lines 3x-2y-1 = 0 and 3x-2y-13 = 0 and is equally distant from both lines.

The problem is almost trivial, with no need to use a formula! They really force you to use specific formulas for it??

Just take the average of the 1 and the 13, if you know how that term in the equations affects the lines.

And I see no reason at all to use any angles. Did they tell you you have to do that, too? If so, you'll have to quote the problem as given, including all those unnecessary requirements and what the formulas you are forced to use mean.

But you can easily get to the answer from where you are. You found the distance to each line from the origin, and you averaged them to find the appropriate distance for the new line. Now just use the formula in reverse.

I have to agree with JeffM, you are not making it easy for people to help you. I understand that part of the issue is a language barrier, but showing us that original problem would help us even if we can't read it, and certainly if you translated it adequately. And showing the solution you are trying to understand is essential, if you have to follow that method.

 

[Steven G]

The answer is simply 3x-2y-(1+13)/2 = 0 or 3x-2y-7 = 0