Parallel & Perpendicular Lines Comparing the slope of 2 lines determines if those lines are...
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Parallel & Perpendicular Lines Comparing the slope of 2 lines determines if those lines are parallel, perpendicular, or just intersecting ( neither ). Parallel Lines – slopes are EQUAL Perpendicular lines – slopes are reciprocal AND opposite signs 2 1 m m 1 2 1 m m
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Transcript of Parallel & Perpendicular Lines Comparing the slope of 2 lines determines if those lines are...
Parallel & Perpendicular Lines
Comparing the slope of 2 lines determines if those lines are parallel, perpendicular, or just intersecting ( neither ).
Parallel Lines – slopes are EQUAL
Perpendicular lines – slopes are reciprocal AND opposite signs
21 mm
121 mm
Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
21 mm
EXAMPLE : Find the slope of all lines parallel to the line on the graph.
( 2 , - 2 )
( 6 , 4 )
Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
21 mm
EXAMPLE : Find the slope of all lines parallel to the line on the graph.
( 2 , - 2 )
( 6 , 4 )
Use the slope formula :
12
12
xx
yym
( x1 , y1 )
( x2 , y2 )
Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
21 mm
EXAMPLE : Find the slope of all lines parallel to the line on the graph.
( 2 , - 2 )
( 6 , 4 )
Use the slope formula :
2
3
4
662
4212
12
m
m
xx
yym
( x1 , y1 )
( x2 , y2 )
Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
21 mm
EXAMPLE : Find the slope of all lines parallel to the line on the graph.
( 2 , - 2 )
( 6 , 4 )
Use the slope formula :
2
3m
( x1 , y1 )
( x2 , y2 )
Parallel lines have the SAME slope…
Answer
Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
21 mm
EXAMPLE : Find the slope of all lines parallel to the line on the graph.
( 2 , - 2 )
( 6 , 4 )
You could have also just counted the slope from the graph…start at one point and count…
+ 6
+ 4
2
3
4
6m
Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
21 mm
EXAMPLE : Find the slope of all lines parallel to the line on the graph.
( 2 , - 2 )
( 6 , 4 )
You could have also just counted the slope from the graph…start at one point and count…
2
3m Answer
+ 6
+ 4
Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
21 mm
EXAMPLE : Find the slope of all lines parallel to 1032 yx
Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
21 mm
EXAMPLE : Find the slope of all lines parallel to 1032 yx
Let’s solve for y and get the equation into y = mx + b form…
3
10
3
23
10
3
2
3
3
1023
2 2
1032
xy
xy
xy
xx
yx
Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
21 mm
EXAMPLE : Find the slope of all lines parallel to 1032 yx
3
10
3
23
10
3
2
3
3
1023
2 2
1032
xy
xy
xy
xx
yx
Let’s solve for y and get the equation into y = mx + b form…
Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
21 mm
EXAMPLE : Find the slope of all lines parallel to 1032 yx
3
10
3
2
3
10
3
2
3
3
1023
2 2
1032
xy
xy
xy
xx
yx
Let’s solve for y and get the equation into y = mx + b form…
Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
21 mm
EXAMPLE : Find the slope of all lines parallel to 1032 yx
3
10
3
2
3
10
3
2
3
3
1023
2 2
1032
xy
xy
xy
xx
yx
Let’s solve for y and get the equation into y = mx + b form…
Here’s the slope…
Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
21 mm
EXAMPLE : Find the slope of all lines parallel to 1032 yx
3
10
3
2
3
10
3
2
3
3
1023
2 2
1032
xy
xy
xy
xx
yx
Let’s solve for y and get the equation into y = mx + b form…
Here’s the slope…
So parallel slope would be the SAME …
3
2m
Answer
Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
EXAMPLE : Find the slope of all lines perpendicular to the line on the graph.
121 mm
( - 6 , - 2 )
( - 1 , - 5 )
( x1 , y1 )
( x2 , y2 )
12
12
xx
yym
Use the slope formula :
Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
EXAMPLE : Find the slope of all lines perpendicular to the line on the graph.
121 mm
( - 6 , - 2 )
( - 1 , - 5 )
( x1 , y1 )
( x2 , y2 )
5
3
61
25
61
2512
12
m
m
xx
yym
Use the slope formula :
Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
EXAMPLE : Find the slope of all lines perpendicular to the line on the graph.
121 mm
( - 6 , - 2 )
( - 1 , - 5 )
( x1 , y1 )
( x2 , y2 )
5
3m
Use the slope formula :
To get the perpendicular slope, flip the fraction and change the sign…
Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
EXAMPLE : Find the slope of all lines perpendicular to the line on the graph.
121 mm
( - 6 , - 2 )
( - 1 , - 5 )
( x1 , y1 )
( x2 , y2 )
5
3m
Use the slope formula :
To get the perpendicular slope, flip the fraction and change the sign…
3
5m
Answer
Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
EXAMPLE : Find the slope of all lines perpendicular to the given equation.
121 mm
72 yx
Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
EXAMPLE : Find the slope of all lines perpendicular to the given equation.
121 mm
2
7
2
1
2
7
22
2
72
72
xy
xy
xy
xx
yxSolve for “y” and get equation into y = mx + b form
Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
EXAMPLE : Find the slope of all lines perpendicular to the given equation.
121 mm
2
7
2
1
2
7
22
2
72
72
xy
xy
xy
xx
yx
2
1m
Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
EXAMPLE : Find the slope of all lines perpendicular to the given equation.
121 mm
2
7
2
1
2
7
22
2
72
72
xy
xy
xy
xx
yx
2
1m
1
2m
To get the perpendicular slope, flip the fraction and change the sign…
Answer
Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
Parallel Lines – slopes are EQUAL
EXAMPLE : Are the given equations parallel, perpendicular, or neither.
121 mm
4
3
3
2
3
5
3
2
xy
xy
21 mm
Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
Parallel Lines – slopes are EQUAL
EXAMPLE : Are the given equations parallel, perpendicular, or neither.
121 mm
4
3
3
2
3
5
3
2
xy
xy
21 mm
Compare the slopes :
- not the same ( different signs )
- not reciprocal
Therefore they are NEITHER
Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
Parallel Lines – slopes are EQUAL
EXAMPLE : Are the given equations parallel, perpendicular, or neither.
121 mm
834 1043 yxyx
21 mm
Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
Parallel Lines – slopes are EQUAL
EXAMPLE : Are the given equations parallel, perpendicular, or neither.
121 mm
3
8
3
4
4
10
4
3
843 1034
834 1043
xyxy
xyxy
yxyx
21 mm
Get both equations into y = mx + b form
Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
Parallel Lines – slopes are EQUAL
EXAMPLE : Are the given equations parallel, perpendicular, or neither.
121 mm
3
8
3
4
4
10
4
3
843 1034
834 1043
xyxy
xyxy
yxyx
21 mm
Compare slopes…
- not the same
- they are reciprocal opposite signs
Perpendicular
