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 :
Step 2 :
Slope of AB :
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 :
Step 2 :
Slope of AB :
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 :
Step 2 :
Slope of AB :
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.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM