   Chapter 10.5, Problem 23E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 9 to 24, find an equation of the line described. Leave the solution in the form Ax+By = C .The line is the perpendicular bisector of the line segment that joins (3, 5) and (5,-1).

To determine

Find the equation of the line which is the perpendicular bisector of the line segment that joins (3, 5) and (5,-1).

Explanation

The midpoint of the line segment M that joins (3, 5) and (5,-1) is calculated as follows,

M=3+525-12

M=8242

M=4, 2

Let m1 be the slope of the line segment that joins (3, 5) and (5,-1)

Let m2 be the slope of the line for which the equation to be found.

The slope m1 is calculated using the relationship m=y-y1x-x1

Now,

x1=3

y1=5

x=5

y=-1

Substitute x1, y1, x and y to find the slope.

So,

m1=-1-55-3

m1=-62

m1=-3

Since slope of the unknown line is perpendicular to the line segment

m2=-1m1

Then

m2=-1

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