Shrunk AxesDate: 01/20/97 at 10:31:59 From: Jen Subject: Coordinate axes When using the distance formula, suppose that the coordinate axes are not perpendicular, but they form some other angle (say 60 deg). How would you find the distance between points in this system? I was thinking about using Law of Sines or Cosines, but I am not really sure. Date: 01/20/97 at 13:34:58 From: Doctor Ken Subject: Re: Coordinate axes Hi there - To answer this question, you've got to go back and do some thinking about what you mean by the question. The reason is that when we use coordinate axes, we essentially *define* the axes to be perpendicular. This question gets answered in an area of math called "Linear Algebra," which is usually taught in the first couple of years of college. The answer is that there are a few different ways to measure the distance, depending on what you meant by the question, and they give you different results! But here's one way: just pretend you're in the regular system. For instance, if we have these points: / / 3-/- / / 2-/- *B = (4,2) / / 1-/- *A = (1,1) / / -------/-----/-----/-----/-----/-----/-----/-----/-----/---> / 1 2 3 4 5 6 7 8 / See how I measured the coordinates by using a grid parallel to the two axes? So once you have these coordinates, you can find the distance *relative to this coordinate system* by using the regular old distance formula. Here we have Sqrt{(4-1)^2 + (2-1)^2} = Sqrt{10} as the distance. If we wanted to find the distance between these points in the *regular* coordinate system, we'd first have to find the coordinates of these points in the regular system, and then use the distance formula. You can find more information about this in the College Linear Algebra section of our archives at: http://mathforum.org/dr.math/tocs/linearal.college.html -Doctor Ken, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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