FINDING EQUATION OF PERPENDICULAR BISECTOR

A perpendicular bisector of a line segment is a line segment perpendicular to and passing through the midpoint of the line.

To find equation of perpendicular bisector, we follow the steps given below.

Step 1 :

Find the midpoint of the line segment for which we have to find the perpendicular bisector.

Step 2 :

Find the slope of the line segment.

Step 3 :

Find the slope of the perpendicular line using the formula -1/m. Here m is slope of the given line.

Step 4 :

To find equation of the perpendicular line, we use the formula given below.

(y - y1) = -1/m (x - x1)

Write an equation for the perpendicular bisector of the line segment joining

Problem 1 :

A(1, 4) and B(6, -6)

Solution :

Step 1 :

Midpoint of AB :

x1=1, x2=6, y1=4, y2=-6Midpoint =(x1+x2)2, (y1+y2)2=(1+6)2, (4-6)2=72, -22=72,-1

Step 2 :

Slope of AB :

Slope (m)=y2-y1x2-x1m= -6-46-1m= -105=-2

Step 3 :

Slope of perpendicular line = -1/m

= -1/-2

= 1/2

Step 4 :

Equation of the perpendicular bisector of AB

y - y1 = m(x - x1)

y + 1 = 1/2(x - 7/2)

2(y + 1) = (x - 7/2)

2y + 2 = (2x - 7)/2

2(2y + 2) = 2x - 7

4y + 4 = 2x - 7

2x - 4y = 4 + 7

2x - 4y = 11

So, equation of perpendicular bisector is 2x - 4y = 11.

Problem 2 :

A(-3, -5) and B(9, -2)

Solution :

Step 1 :

Midpoint of AB :

x1=-3, x2=9, y1=-5, y2=-Midpoint =(x1+x2)2, (y1+y2)2=(-3+9)2, (-5-2)2=62, -72=3, -72

Step 2 :

Slope of AB :

Slope (m)=y2-y1x2-x1m= -2+59+3m= 312= 14

Step 3 :

Slope of perpendicular line = -1/m

= -1/(1/4)

= -4

Step 4 :

Equation of the perpendicular bisector of AB

y - y1 = m(x - x1)

y + 7/2 = -4(x - 3)

(2y + 7)/2 = -4x + 12

2y + 7 = 2(-4x + 12)

2y + 7 = -8x + 24

8x + 2y = 24 - 7

8x + 2y = 17

So, equation of perpendicular bisector is 8x + 2y = 17.

Problem 3 :

A(5, 10) and B(10, 7)

Solution :

Step 1 :

Midpoint of AB :

x1=5, x2=10, y1=10, y2=Midpoint =(x1+x2)2, (y1+y2)2=(5+10)2, (10+7)2=152, 172

Step 2 :

Slope of AB :

Slope (m)=y2-y1x2-x1m= 7-1010-5m= -35

Step 2 :

Slope of the line joining the point A and B.

m = (y2 - y1)/(x2 - x1)

m = (7 - 10)/(10 - 5)

m = -3/5

Step 3 :

Slope of perpendicular line = -1/m

= -1/(-3/5)

= 5/3

Step 4 :

Equation of the perpendicular bisector of AB

y - y1 = m(x - x1)

y - 17/2 = 5/3(x - 15/2)

3(2y - 17)/2 = 5(x - 15/2)

(6y - 51)/2 = (5x - 75/2)

(6y - 51)/2 = (10x - 75)/2

6y - 51 = 10x - 75

10x - 6y = 75 - 51

10x - 6y = 24

So, equation of perpendicular bisector is10x - 6y = 24.

Recent Articles

  1. Finding Range of Values Inequality Problems

    May 21, 24 08:51 PM

    Finding Range of Values Inequality Problems

    Read More

  2. Solving Two Step Inequality Word Problems

    May 21, 24 08:51 AM

    Solving Two Step Inequality Word Problems

    Read More

  3. Exponential Function Context and Data Modeling

    May 20, 24 10:45 PM

    Exponential Function Context and Data Modeling

    Read More