Perpendicular Bisector of a Line To find the equation of the perpendicular bisector of a line...
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Transcript of Perpendicular Bisector of a Line To find the equation of the perpendicular bisector of a line...
![Page 1: 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.](https://reader038.fdocuments.in/reader038/viewer/2022110402/56649e405503460f94b32300/html5/thumbnails/1.jpg)
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
![Page 2: 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.](https://reader038.fdocuments.in/reader038/viewer/2022110402/56649e405503460f94b32300/html5/thumbnails/2.jpg)
Perpendicular Bisector of a Line
EXAMPLE : Find the equation of the perpendicular bisector of the line segment with endpoints ( 2 , 7 ) and ( 4 , - 1 ).
![Page 3: 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.](https://reader038.fdocuments.in/reader038/viewer/2022110402/56649e405503460f94b32300/html5/thumbnails/3.jpg)
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
![Page 4: 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.](https://reader038.fdocuments.in/reader038/viewer/2022110402/56649e405503460f94b32300/html5/thumbnails/4.jpg)
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
![Page 5: 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.](https://reader038.fdocuments.in/reader038/viewer/2022110402/56649e405503460f94b32300/html5/thumbnails/5.jpg)
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
![Page 6: 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.](https://reader038.fdocuments.in/reader038/viewer/2022110402/56649e405503460f94b32300/html5/thumbnails/6.jpg)
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
![Page 7: 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.](https://reader038.fdocuments.in/reader038/viewer/2022110402/56649e405503460f94b32300/html5/thumbnails/7.jpg)
Perpendicular Bisector of a Line
EXAMPLE : Find the equation of the perpendicular bisector of the line segment with endpoints ( 0 , 3 ) and ( - 3 , 9 ).
![Page 8: 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.](https://reader038.fdocuments.in/reader038/viewer/2022110402/56649e405503460f94b32300/html5/thumbnails/8.jpg)
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
![Page 9: 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.](https://reader038.fdocuments.in/reader038/viewer/2022110402/56649e405503460f94b32300/html5/thumbnails/9.jpg)
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
![Page 10: 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.](https://reader038.fdocuments.in/reader038/viewer/2022110402/56649e405503460f94b32300/html5/thumbnails/10.jpg)
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
![Page 11: 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.](https://reader038.fdocuments.in/reader038/viewer/2022110402/56649e405503460f94b32300/html5/thumbnails/11.jpg)
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