Equation of Perpendicular Bisector

  1. 1. The problem statement, all variables and given/known data

    Write an equation of the perpendicular bisector of the segment joining the points (7,0) and (1,8).


    2. Relevant equations

    Midpoint formula, Perpendicular slope (negative reciprocal of a line is the slope of a line perpendicular to the first line)

    3. The attempt at a solution

    First I get the slope of the line:
    m = (8-0)/(1-7) = 8/-6 = -4/3

    Then I take the negative reciprocal of it:
    m[perpendicular line] = 3/4

    Then I use the midpoint formula between the two given points, to find a point on the perpendicular line.
    midpoint = (1+7)/2, (8+0)/2
    = (4,4)

    so I now have the line y=(3/4)x + b as the line. I plug in 4,4
    4 = 3/4(4) + b
    I solve b to be 1 (b = 1)

    so now I have y = 3/4 (x) + 1 as the line.

    I'm supposed to give the answer in standard form, so I do:
    m =-A/B = 3/4 to get
    A = -3
    B = 4

    and b = C/B = 1 to get
    b = 1 = C/4
    so C = 4

    So my final answer is -3x + 4y = 4
    However the correct answer in the back of the book is -3x + 4y = -4

    What am I doing wrong?
    Thanks for reading.
     
  2. jcsd
  3. G01

    G01 2,687
    Homework Helper

    Your work is correct for the points you supplied. It is probably a textbook error.
     
  4. your slope calculation is wrong in the beginning :)
     
  5. no it isnt. he's done it right. it must be a textbook error.
     
  6. HallsofIvy

    HallsofIvy 40,310
    Staff Emeritus
    Science Advisor

    Certainly the midpoint is (4, 4) and (4, 4) satisfies -3x+ 4y= 4, not -3x+ 4y= -4.
     
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