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Equation of Perpendicular Bisector 
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#1
Sep907, 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 = (80)/(17) = 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
Sep907, 12:47 PM

HW Helper
P: 2,688

Your work is correct for the points you supplied. It is probably a textbook error.



#3
Mar709, 11:16 PM

P: 1

your slope calculation is wrong in the beginning :)



#4
Mar709, 11:25 PM

P: 311

Equation of Perpendicular Bisector



#5
Mar809, 05:44 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,327

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



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