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Equation of Perpendicular Bisector

by TbbZz
Tags: bisector, equation, perpendicular
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Sep9-07, 11:01 AM
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.
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Sep9-07, 12:47 PM
HW Helper
G01's Avatar
P: 2,685
Your work is correct for the points you supplied. It is probably a textbook error.
Mar7-09, 11:16 PM
P: 1
your slope calculation is wrong in the beginning :)

Mar7-09, 11:25 PM
P: 311
Equation of Perpendicular Bisector

Quote Quote by sarahmaliha View Post
your slope calculation is wrong in the beginning :)
no it isnt. he's done it right. it must be a textbook error.
Mar8-09, 05:44 AM
Sci Advisor
PF Gold
P: 39,557
Certainly the midpoint is (4, 4) and (4, 4) satisfies -3x+ 4y= 4, not -3x+ 4y= -4.

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