Distance from origin : GMAT Quantitative Section
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# Distance from origin

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Manager
Joined: 11 Jul 2010
Posts: 227
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Is the following a property of the coordinate system? If [#permalink]

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25 Jul 2010, 05:42
Is the following a property of the coordinate system?

If (r,s) and (u,v) - two points - have the same coordinates in reverse order

i.e., (r,s) and (s,r) [u=s; v=r]

then points (r,s) and (u,v) will be equidistant from the origin (0,0) --- I read this an an explanation for Q. 164 (OG 12th ed) in the MGMAT companion to OG...

and couldn't completely follow why this would always be so...
Math Expert
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25 Jul 2010, 05:53
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Expert's post
gmat1011 wrote:
Is the following a property of the coordinate system?

If (r,s) and (u,v) - two points - have the same coordinates in reverse order

i.e., (r,s) and (s,r) [u=s; v=r]

then points (r,s) and (u,v) will be equidistant from the origin (0,0) --- I read this an an explanation for Q. 164 (OG 12th ed) in the MGMAT companion to OG...

and couldn't completely follow why this would always be so...

Distance between the point $$(x,y)$$ and the origin can be found by the formula: $$D=\sqrt{x^2+y^2}$$.

So the distance between the point $$(r,s)$$ and the origin would be $$D=\sqrt{r^2+s^2}$$, and the distance between the point $$(s,r)$$ and the origin would be $$D=\sqrt{s^2+r^2}$$, which is the same.

For more please check Coordinate Geometry chapter of Math Book (link in my signature).

Hope it helps.
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Joined: 11 Jul 2010
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Kudos [?]: 88 [0], given: 20

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25 Jul 2010, 07:33
great - thanks bunuel

as always, very grateful for all the resources you have put together!
Re: Distance from origin   [#permalink] 25 Jul 2010, 07:33
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