# Equation of Perpendicular Bisector

by TbbZz
Tags: bisector, equation, perpendicular
 P: 37 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.
 HW Helper PF Gold P: 2,688 Your work is correct for the points you supplied. It is probably a textbook error.
 P: 1 your slope calculation is wrong in the beginning :)
P: 311

## Equation of Perpendicular Bisector

 Quote by sarahmaliha your slope calculation is wrong in the beginning :)
no it isnt. he's done it right. it must be a textbook error.
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,707 Certainly the midpoint is (4, 4) and (4, 4) satisfies -3x+ 4y= 4, not -3x+ 4y= -4.

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