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

Zeeshan 01
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Registered: 2016-07-22
Posts: 746

Distance between parallel line

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


Malik

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

tanith
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Registered: 2017-04-26
Posts: 9

Re: Distance between parallel line

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

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

Zeeshan 01
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Registered: 2016-07-22
Posts: 746

Re: Distance between parallel line

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)


Malik

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

tanith
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Registered: 2017-04-26
Posts: 9

Re: Distance between parallel line

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.

bi429C4.png

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

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

Zeeshan 01
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Registered: 2016-07-22
Posts: 746

Re: Distance between parallel line

Your sign is wrong in 2x?


Malik

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

Bob
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Registered: 2010-06-20
Posts: 10,053

Re: Distance between parallel line

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


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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

tanith
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Registered: 2017-04-26
Posts: 9

Re: Distance between parallel line

You are right smile

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

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

Zeeshan 01
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Registered: 2016-07-22
Posts: 746

Re: Distance between parallel line

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


Malik

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

Bob
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Registered: 2010-06-20
Posts: 10,053

Re: Distance between parallel line

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


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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

Zeeshan 01
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Registered: 2016-07-22
Posts: 746

Re: Distance between parallel line

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


Malik

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

Zeeshan 01
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Registered: 2016-07-22
Posts: 746

Re: Distance between parallel line

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


Malik

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

Bob
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Registered: 2010-06-20
Posts: 10,053

Re: Distance between parallel line

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

note the bracket:

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

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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

Zeeshan 01
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Registered: 2016-07-22
Posts: 746

Re: Distance between parallel line

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


Malik

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

Zeeshan 01
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Registered: 2016-07-22
Posts: 746

Re: Distance between parallel line

Can u put in formula


Malik

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