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Coordinate Geometry and line equation

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    Here is a question which I need help on:

    Find the equation of the straight line (in the form ax+by+c=0 where a,b and c are integers) which is the perpendicular bisector the line through (4,9) and (-2,1).

    Here are the main parts of my long working out:

    I found the midpoint of the line through (4,9) and (-2,1) to be (1,5)

    (1,5)=(x1, y1)

    The gradient of the line through (4,9) and (-2,1) is \frac{8}{6}
    Therefore the gradient of the perpendicular bisector must be -\frac{6}{8}

    y-5=-\frac{6}{8}(x-1)

    y-5=-\frac{6}{8}x+\frac{6}{8}

    8(y-5)=-6x+6

    Therefore my answer is the following:
    6x+8y-46=0

    This is incorrect, because the correct answer is 3x+4y-23=0:confused:
    What have I done wrong???:confused::confused:

    Thanks a lot for any help provided.
  2. Offline

    (Original post by krisshP)
    Here is a question which I need help on:

    Find the equation of the straight line (in the form ax+by+c=0 where a,b and c are integers) which is the perpendicular bisector the line through (4,9) and (-2,1).

    Here are the main parts of my long working out:

    I found the midpoint of the line through (4,9) and (-2,1) to be (1,5)

    (1,5)=(x1, y1)

    The gradient of the line through (4,9) and (-2,1) is \frac{8}{6}
    Therefore the gradient of the perpendicular bisector must be -\frac{6}{8}

    y-5=-\frac{6}{8}(x-1)

    y-5=-\frac{6}{8}x+\frac{6}{8}

    8(y-5)=-6x+6

    Therefore my answer is the following:
    6x+8y-46=0

    This is incorrect, because the correct answer is 3x+4y-23=0:confused:
    What have I done wrong???:confused::confused:

    Thanks a lot for any help provided.
    You haven't done anything wrong, I don't think. They've just divided the equation by two or simplified the perpendicular bisector gradient -\frac{6}{8} to -\frac{3}{4}

    Your answer is still fine, though
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    (Original post by usycool1)
    You haven't done anything wrong, I don't think. They've just divided the equation by two
    So if my answer to this type of question is simply a multiple of the correct answer, does this mean I will be correct always in this case?
  4. Offline

    (Original post by krisshP)
    So if my answer to this type of question is simply a multiple of the correct answer, does this mean I will be correct always in this case?
    It should be OK as usually in a mark scheme it says "oe" next to the answer which means "or equivalent"
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    (Original post by usycool1)
    It should be OK as usually in a mark scheme they write "oe" next to the answer which means "or equivalent"
    It's just that I haven't done any past papers for A-level Maths - the only practice is from a revision book.

    Thanks a LOT for your help
  6. Offline

    (Original post by krisshP)
    It's just that I haven't done any past papers for A-level Maths - the only practice is from a revision book.

    Thanks a LOT for your help
    I see

    No problem

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