Distance between parallel line

Zeeshan 01 · 2017-04-26 02:51:12

Hi;
What is distance between parallel line ???
And question

Find distance between parallel lines
Line 1 : 2x-5y+13=0
Line 2: 2x-5y+6=0

tanith · 2017-04-26 03:40:53

Well, let's say we have two parallel lines

We would figure out whether they are parallel or not by looking for a point where they meet, i.e.

Obviously this is not correct so there is no point where they meet, i.e. they are parallel.

We would calculate the distance by taking the difference between these two lines

Zeeshan 01 · 2017-04-26 04:20:10

Can u please explain according to question how I subtract this in my question

Last edited by Zeeshan 01 (2017-04-26 04:21:25)

tanith · 2017-04-26 19:27:04

You have two equations with two variables each.
You can plot these in a two-dimensional coordinate system with the axes x and y.

In this case it would be sensible to rewrite the equations in such a way that you could plot them by plugging in numbers, e.g.

You can see that you have a linear equation. And then you do the same with the other equation and take the difference.

Last edited by tanith (2017-04-26 20:23:49)

Zeeshan 01 · 2017-04-26 20:09:51

Your sign is wrong in 2x?

Bob · 2017-04-26 20:22:21

Your sign is wrong in 2x?

Maybe this was deliberate so that you could work your question on your own rather than just copy a model answer. Anyway, why does it matter? You wanted to be shown the method and you have been shown.

Bob

tanith · 2017-04-26 20:25:08

You are right

I edited my post and removed the mistake. So what is the distance between these two parallel lines?

Zeeshan 01 · 2017-04-27 13:47:35

How to put in distance formula tanith there is no (x1,y1)???

Bob · 2017-04-27 19:21:57

If you want to do this using that formula you need (x1,y1) to be (any) point on one line, and (x2,y2) to be a nearest point to it on the other line. You could proceed like this:

step 1: choose a point on line 1 ; A = (x1,y1)
step 2: calculate the gradient of the line through A perpendicular to line 1.
step 3: calculate the equation of the perpendicular line (say, line P)
step 4: calculate where line 2 crosses line P ; B = (x2,y2)
step 5: calculate the length of AB.

I think it is quicker to calculate the difference between the intercepts = D. Then the angle of slope of the lines, θ. Then the required distance is D.cos(θ)

There is also a formula for calculating the distance from a known point to a known line. Ask again if you want this formula.

Bob

Zeeshan 01 · 2017-04-27 21:03:09

D=ax1+by1+c/sqrt (a^2+b^2)

Zeeshan 01 · 2017-04-27 21:04:09

Can I put in this because this Is in book???

Bob · 2017-04-27 21:06:59

Yes. That's the formula I was referring to.

note the bracket:

D=(ax1+by1+c)/sqrt (a^2+b^2)

Bob

Zeeshan 01 · 2017-04-28 14:42:43

Yes bracket is D=(ax1+by1+c)/sqrt (a^2+b^2)

Zeeshan 01 · 2017-04-30 20:57:27

Can u put in formula

Math Is Fun Forum

#1 2017-04-26 02:51:12

Distance between parallel line

#2 2017-04-26 03:40:53

Re: Distance between parallel line

#3 2017-04-26 04:20:10

Re: Distance between parallel line

#4 2017-04-26 19:27:04

Re: Distance between parallel line

#5 2017-04-26 20:09:51

Re: Distance between parallel line

#6 2017-04-26 20:22:21

Re: Distance between parallel line

#7 2017-04-26 20:25:08

Re: Distance between parallel line

#8 2017-04-27 13:47:35

Re: Distance between parallel line

#9 2017-04-27 19:21:57

Re: Distance between parallel line

#10 2017-04-27 21:03:09

Re: Distance between parallel line

#11 2017-04-27 21:04:09

Re: Distance between parallel line

#12 2017-04-27 21:06:59

Re: Distance between parallel line

#13 2017-04-28 14:42:43

Re: Distance between parallel line

#14 2017-04-30 20:57:27

Re: Distance between parallel line

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