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(-3, 4) and B(5, 6)
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 - 5 = -4(x - 1)
y = -4x + 4 + 5
y = -4x + 9
So, equation of perpendicular bisector is y = -4x + 9.
Problem 2 :
A(3, 8) and B(7, 14)
Solution :
Step 1 :
Midpoint of AB :
Step 2 :
Slope of AB :
Step 3 :
Slope of perpendicular line = -1/m
= -1/(3/2)
= -2/3
Step 4 :
Equation of the perpendicular bisector of AB
y - y1 = m(x - x1)
y - 11 = -2/3(x - 5)
3(y - 11) = -2(x - 5)
3y - 33 = -2x + 10
2x + 3y = 10 + 33
2x + 3y = 43
So, equation of perpendicular bisector is 2x + 3y = 43.
Problem 3 :
A(-5, 6) and B(1, 8)
Solution :
Step 1 :
Midpoint of AB :
Step 2 :
Slope of AB :
Step 3 :
Slope of perpendicular line = -1/m
= -1/(1/3)
= -3
Step 4 :
Equation of the perpendicular bisector of AB
y - y1 = m(x - x1)
y - 7 = -3(x + 2)
y - 7 = -3x - 6
3x + y = 7 - 6
3x + y = 1
y = -3x + 1
So, equation of perpendicular bisector is y = -3x + 1.
Problem 4 :
A(-3, -6) and B(-1, 2)
Solution :
Step 1 :
Midpoint of AB :
Step 2 :
Slope of AB :
Step 3 :
Slope of perpendicular line = -1/m
= -1/4
Step 4 :
Equation of the perpendicular bisector of AB
y - y1 = m(x - x1)
y + 2 = -1/4(x + 2)
4(y + 2) = -1(x + 2)
4y + 8 = -x - 2
x + 4y = -8 - 2
x + 4y = -10
So, equation of perpendicular bisector is x + 4y = -10.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM