(adsbygoogle = window.adsbygoogle || []).push({}); 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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# Equation of Perpendicular Bisector

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