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Math Help - loci

  1. #1
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    loci

    How many points are there in a plane that are 4 centimeters from a given line and also 5 centimeters from a given point on that line?
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  2. #2
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    Hello, blame_canada100!

    Did you make a sketch?


    How many points are there in a plane that are 4 cm from a given line
    and also 5 cm from a given point on that line?

    All points which are 4 cm from line L are on a pair of lines
    . . parallel to and 4 cm from line L.
    Code:
      - - - - - - - - - - - - - -
      :
      4
      :
     ---------------------------- L
      :
      4
      :
      - - - - - - - - - - - - - -

    Given a point P on line L, there are four points
    . . which are on the two lines and 5 cm from P.
    Code:
      - - - - o - - - o - - - -
      :        \     /
      4        5\   /5
      :          \ /
     -------------*------------ L
      :          /P\
      4        5/   \5
      :        /     \
      - - - - o - - - o - - - -
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