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Perpendicular Bisector of a Line
To find the equation of the perpendicular bisector of a line segment :
1. Find the midpoint
2. Find the slope of the given line segment
3. Find the perpendicular slope ( flip the fraction and change signs )
4. Use the midpoint ( a , b ) and the perpendicular slope in the
point – slope equation.
2
,2
midpoint 2121 yyxx
12
12
xx
yym
baxmy
Perpendicular Bisector of a Line
EXAMPLE : Find the equation of the perpendicular bisector of the line segment with endpoints ( 2 , 7 ) and ( 4 , - 1 ).
Perpendicular Bisector of a Line
EXAMPLE : Find the equation of the perpendicular bisector of the line segment with endpoints ( 2 , 7 ) and ( 4 , - 1 ).
1. 3,32
6,
2
6
2
)1(7,
2
42
2,
2 midpoint 2121
yyxx
Perpendicular Bisector of a Line
EXAMPLE : Find the equation of the perpendicular bisector of the line segment with endpoints ( 2 , 7 ) and ( 4 , - 1 ).
1.
2.
3,32
6,
2
6
2
)1(7,
2
42
2,
2 midpoint 2121
yyxx
1
4
2
8
24
71
12
12
xx
yym
Perpendicular Bisector of a Line
EXAMPLE : Find the equation of the perpendicular bisector of the line segment with endpoints ( 2 , 7 ) and ( 4 , - 1 ).
1.
2.
3.
3,32
6,
2
6
2
)1(7,
2
42
2,
2 midpoint 2121
yyxx
1
4
2
8
24
71
12
12
xx
yym
4
1m
Perpendicular Bisector of a Line
EXAMPLE : Find the equation of the perpendicular bisector of the line segment with endpoints ( 2 , 7 ) and ( 4 , - 1 ).
1.
2.
3.
4.
3,32
6,
2
6
2
)1(7,
2
42
2,
2 midpoint 2121
yyxx
1
4
2
8
24
71
12
12
xx
yym
4
1m
334
1
xy
baxmy Substitute the midpoint and perpendicular slope into point – slope form
Perpendicular Bisector of a Line
EXAMPLE : Find the equation of the perpendicular bisector of the line segment with endpoints ( 0 , 3 ) and ( - 3 , 9 ).
Perpendicular Bisector of a Line
EXAMPLE : Find the equation of the perpendicular bisector of the line segment with endpoints ( 0 , 3 ) and ( - 3 , 9 ).
1.
6,2
3
2
12,
2
3
2
93,
2
)3(0
2,
2 midpoint 2121 yyxx
Perpendicular Bisector of a Line
EXAMPLE : Find the equation of the perpendicular bisector of the line segment with endpoints ( 0 , 3 ) and ( - 3 , 9 ).
1.
2.
6,2
3
2
12,
2
3
2
93,
2
)3(0
2,
2 midpoint 2121 yyxx
1
2
3
6
03
39
12
12
xx
yym
Perpendicular Bisector of a Line
EXAMPLE : Find the equation of the perpendicular bisector of the line segment with endpoints ( 0 , 3 ) and ( - 3 , 9 ).
1.
2.
3.
6,2
3
2
12,
2
3
2
93,
2
)3(0
2,
2 midpoint 2121 yyxx
1
2
3
6
03
39
12
12
xx
yym
2
1m
Perpendicular Bisector of a Line
EXAMPLE : Find the equation of the perpendicular bisector of the line segment with endpoints ( 0 , 3 ) and ( - 3 , 9 ).
1.
2.
3.
4.
6,2
3
2
12,
2
3
2
93,
2
)3(0
2,
2 midpoint 2121 yyxx
1
2
3
6
03
39
12
12
xx
yym
2
1m
62
3
2
1
62
3
2
1
xy
xy
baxmy
Substitute the midpoint and perpendicular slope into point – slope form
