# To find the equation of the perpendicular bisector of the line segment joining the points A ( 1 , 4 ) and B ( 7 , − 2 )

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter B, Problem 45E
To determine

## To calculate: To find the equation of the perpendicular bisector of the line segment joining the points A(1,4) and B(7,−2)

Expert Solution

The equation of perpendicular bisector is y=x3

### Explanation of Solution

Given information: Points are A(1,4) and B(7,2)

Formula Used:

The mid-point of the line segment from P1(x1,y1) to P2(x2,y2) is x1+x22,y1+y22

Product of the slope of perpendicular line is equal to 1

Perpendicular bisector of a line segment is a line that is perpendicular to the line segment and passes through the mid-point of the line segment

Slope of the line passing through the points P1(x1,y1) to P2(x2,y2) is

m=y2y1x2x1

Equation of line having slope m and passing through the point P1(x1,y1) is

yy1=m(xx1)

Calculation:

Points are given as follows:

A(1,4) and B(7,2)

Slope of the line segment is calculated as

m=2471m=66m=1

Let us assume that slope of line perpendicular to above line is m1

Since theProduct of the slope of perpendicular line is equal to 1

Thus,

mm=11

Substituting the values,

m=111m=11

Mid-point of the line segment joining above two points is calculated as

(x,y)=x1+x22,y1+y22

Substituting the values,

(x,y)=1+72,422(x,y)=82,22(x,y)=4,1

Thus, the perpendicular bisector passes through the point (4,1)

Now, equation of perpendicular bisector is

y1=1(x4)y1=x4y=x4+1y=x3

Conclusion:

Hence, equation of perpendicular bisector is y=x3

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