Question

how to find the distances between lines? let's say 2x+3y=6 and 4x+6y=8 ?

Answer 1

first of all the two lines have to be parallel (which these are)

write them in point slope form...

Answer 2

If the lines are parallel, you need to measure a perpendicular distance between them.

Answer 3

okay and what if lines are not parallel?

Answer 4

If they aren't parallel and in fact cross somewhere, then "distance between them" depends on where you want to check... could be big, could be nothing at the intersection.

Answer 5

@jake how to find perpendicular distance ?

Answer 6

Find the slope of each to see if they are parallel (same slope)

Answer 7

that was just an example...okay let's say 2x+4y=9 and 2x+4y=10 now?

Answer 8

Sorry, internet lag here... my responses are showing up with a lot of delay.

Answer 9

that's okay

Answer 10

@amistre64 has the diagram (darn slow internet!!)

Answer 11

@amistre64 do i need to plot that again and again...?

Answer 12

Do you really need to go with "sin(a)" to get this though? Agree that works, but is there a non-trig way?

Answer 13

is there any formula or something

Answer 14

its a general setup to notice what parts you can use

Answer 15

the slope of a line is the tangent of the angle between x axis, so "a" in this case is 90-tan^(-1) (slope)

and b is the difference in y intercepts

Answer 16

which should be the same as the difference between the constants used

Answer 17

@erica.d if you are comfortable with that approach, that works well. Otherwise, you may have some extra work to find points on the "connector line" where it intersects your two original lines, then you could do distance formula with those points.

Answer 18

@JakeV8 thanks...i was just wondering if i could use some formula

Answer 19

Would be nice, wouldn't it ? :)

Answer 20

using:

2x+4y=9
2x+4y=10 ; 10-9 = 1

m = -2/4 = -.5

1*sin(90-arctan(-.5)) is what im thinking :)

Answer 21

Do you know the distance formula between two points?

Answer 22

might have to reconsider my "constants"

10/4 - 9/4 = 1/4 ... not 1 sooo

Answer 23

@amistre64 I'm taking notes :) I hadn't thought of your approach :)

Answer 24

thanks @amistre64 @JakeV8

Answer 25

:) i get .15 if we have something to compare with

Answer 26

im thinking i can make it simpler with a cosine ....

b cos(arctan(m))

Answer 27

Yes, there is a formula for this

Answer 28

You can read more about it here:
http://tinyurl.com/9lk9cwu

Answer 29

@Hero That's a great page... thanks for the link!

Answer 30

@JakeV8, that's my blog. I wrote it.

Answer 31

Writing it is much more awesome than "googling" it... you can find help lots of places, but to create your own is pretty cool.