   Chapter 10.5, Problem 24E 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 (-4, 5) and (1, 1).

To determine

Find the equation of the line which is the perpendicular bisector of the line segment that joins (-4, 5) and (1, 1).

Explanation

The midpoint of the line segment M that joins (-4, 5) and (1, 1) is calculated as follows,

M=-4+125+12

M=-3262

M=-32, 3

Let m1 be the slope of the line segment that joins (-4, 5) and (1, 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=-4

y1=5

x=1

y=1

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

So,

m1=1-51-(-4)

m1=-41+4

m1=-45

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

m2=-1m1

Then

m2=-1-45

m2=54

The unknown line equation can be found using its slope m2=54 and midpoint M=-32, 3 using the relationship y-y1=m(x-x1)

Now, x1=-32

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