distance of a line ax+by+c=0 from (0,0)

kishore: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Fri Dec 21, 2007 2:58 pm; Location: Fremont , California; Thanked: 3 times

by kishore » Wed Jun 04, 2008 10:49 am

formula for distance of a line ax+by+c=0 from (0,0) is
dist = Mod(c/sqrt(a^2+b^2))

or

dist = |c/sqrt(a^2+b^2)|

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Ian Stewart: GMAT Instructor; Posts: 2621; Joined: Mon Jun 02, 2008 3:17 am; Location: Montreal; Thanked: 1090 times; Followed by:355 members; GMAT Score:780

by Ian Stewart » Wed Jun 04, 2008 10:55 am

Yeah, I just derived the formula, and that's correct (with the absolute value included).

I can't imagine a situation where you'd need this on the GMAT, however.

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gabriel: Legendary Member; Posts: 986; Joined: Wed Dec 20, 2006 11:07 am; Location: India; Thanked: 51 times; Followed by:1 members

Re: distance of a line ax+by+c=0 from (0,0)

by gabriel » Wed Jun 04, 2008 11:33 am

netigen wrote:Can someone confirm this formula

formula for distance of a line ax+by+c=0 from (0,0) is
dist = c/sqrt(a^2+b^2)

That is the formula for the perpendicular distance of (0,0) from the line.

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getneonow: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Fri Mar 14, 2008 1:56 am; Location: India; Thanked: 4 times; GMAT Score:730

Re: distance of a line ax+by+c=0 from (0,0)

by getneonow » Thu Jun 05, 2008 12:22 am

gabriel wrote:
netigen wrote:Can someone confirm this formula

formula for distance of a line ax+by+c=0 from (0,0) is
dist = c/sqrt(a^2+b^2)
That is the formula for the perpendicular distance of (0,0) from the line.

when you say distance between a point and a line , it is implied that the distance is the perpendicular distance..

anyways it always helps to have clarity on things..

Neo

MBA : My passion and My pursuit

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gmatinjuly: Master | Next Rank: 500 Posts; Posts: 101; Joined: Tue May 27, 2008 6:03 am; Thanked: 5 times

by gmatinjuly » Mon Jun 09, 2008 4:13 am

Just adding some extra info here.

Dist formula from my point (x1,y1) for a line ax+by +c = 0 is

Mod [ (ax1+by1+c)/(sqrt (a^2+b^2) ]

Here x 1 = 0 and y1 = 0

so

Mod [ c/(sqrt (a^2+b^2) ]

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