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Thread: Simple question on lines.

  1. #1
    Aug 2013

    Simple question on lines.

    Explain why two straight lines in spacecan intersect at most at one point.

    We know that a line is composed of aninfinite set of points. Now, we have line A and line B.(Of the samelenght, but it doesn't matter)

    We will have line A, which isstationary, with any desidered position.

    Now, we will have line B, which will bemobile. I will show you that a line can intersect at most at onepoint. But to be able to do it, we will try to see what happens whenwe try to intersect it at more than one point. We have point a and bat the end of line B and we have have point c on one end of line A.We will put point a on point c. Now, we will put point b on the end of line A,and create a new point called d. We see that the two line are one.Another example, and this time we will have point e in the middle ofline B. Point a on point c.Point e on line A.Now, if we don't putpoint b on point d, this will create a broken line, which will beincorrect. So point b on d. Again, two lines make one line. As we cansee, the moment we intersect a second point with a straight line, wewill have two lines making only one line. So, two straight lines canonly intersect at most one point.

    What do you think of my answer ???
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  2. #2
    MHF Contributor
    Sep 2012

    Re: Simple question on lines.

    Hey Philomath.

    You can set up a linear system and show that it can intersect only at most at one point if you want a more rigorous explanation.
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