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90 Degree Rotations
Beigesteuert von: Smith
2
-2
4
-4
2
-2
4
-4
6
-6
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 When (x,y) is rotated
180 degrees
about the origin,
its new image is:
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( -x,-y )
C'
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A'
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B'
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A (4,4) → A' (-4,-4)

B (3,1) → B' (-3,-1)

C (5,1) → C' (-5,-1)
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B
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A
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C
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2
-2
4
-4
2
-2
4
-4
6
-6
When you rotate a point
about the origin,
The origin is the
point of rotation
B'
A 180 degree rotation
about the origin forms

a            angle (line)
When you connect
the preimage B and
image B' thru the origin
B
2
-2
4
-4
2
-2
4
-4
6
-6
A 90 degree rotation
about the origin forms

a          right angle
When you connect
the preimage B and
image B' thru the origin
When you rotate a point
about the origin,
The origin is the
point of rotation
B'
B
2
-2
4
-4
2
-2
4
-4
6
-6
Each time you rotate
a point 180 degrees
about the origin,

BOTH the x and
coordinates change sign
(-3,-1)
B'
Each time you rotate
a point 360 degrees
about the origin,

the x and y coordinates
remain the SAME
B
(3,1)
2
-2
4
-4
2
-2
4
-4
6
-6
Rotation:      0 (none)           180             360
Location:
(-3,-1)
(3,1)
B'
(-3,-1)
B
(3,1)
(3,1)
Click
OK
2
-2
4
-4
2
-2
4
-4
6
-6
(-5,-1)
Rotation:      0 (none)            180              360
Location:
B'
(5,1)
(     ,      )
(      ,      )
B
(5,1)
2
-2
4
-4
2
-2
4
-4
6
-6
Rotation:      0 (none)      90         180
Location:
(-3,-1)
.
(3,1)
(1,-3)
.
.
(-3,-1)
B'
(1,-3)
B
.
(3,1)
.
Click on the
90 degree
rotation
Rotation:          0       90       180       270     360
Location:
The pattern
for 90 degree
rotations
about the origin
is similar to
connecting
dominoes....
(3,1)
(1,-3)
(-3,-1)
(-1,3)
(3,1)
Rotation:          0       90       180       270      360
Location:
First, write
the points for
180 degree
(opposite x and y)
and 360 degree
(same as original)
rotations.
(3,1)
(-3,-1)
(3,1)
Then, fill in the
blanks
(90 and 270 degrees)
by connecting
matching coordinates.
Rotation:          0       90       180       270     360
Location:
(3,1)
(1,-3)
matching numbers
(-3,-1)
(-1,3)
(3,1)
Location
Rotation
1.
To rotate the original image point (2,5) about the origin:
Fill in the points for a 180 degree (opposite)
and 360 degree (same as original) rotation.
(2,5)
 0            90         180        270       360
(-2,-5)
?
(2,5)
?
Location
Rotation
1.
2.
To rotate the original image point (2,5) about the origin:
Fill in the points for a 180 degree (opposite)
and 360 degree (same as original) rotation.
Fill in the 90 and 270 degree rotations
by connecting matching coordinates.
(2,5)
 0            90         180        270       360
(5,-2)
?
(-2,-5)
(-5,2)
?
(2,5)
Location
Rotation
(2,5)
 0            90         180        270       360
connect
5 and 5
(5,-2)
connect
-2 and -2
(-2,-5)
connect
-5 and -5
(-5,2)
connect
2 and 2
(2,5)
Location
Rotation
1.
To rotate the original image point (4,3) about the origin:
Fill in the points for a 180 degree (opposite)
and 360 degree (same as original) rotation.
(4,3)
 0            90         180        270       360
(-4,-3)
?
(4,3)
?
Location
Rotation
1.
2.
To rotate the original image point (4,3) about the origin:
Fill in the points for a 180 degree (opposite)
and 360 degree (same as original) rotation.
Fill in the 90 and 270 degree rotations
by connecting matching coordinates.
(4,3)
 0            90         180        270       360
(3,-4)
?
(-4,-3)
(-3,4)
?
(4,3)
Location
Rotation
1.
2.
To rotate the original image point (7,-5) about the origin:
Fill in the points for a 180 degree (opposite)
and 360 degree (same as original) rotation.
Fill in the 90 and 270 degree rotations
by connecting matching coordinates.
(7,-5)
 0            90         180        270       360
(-5,-7)
?
(-7,5)
?
(5,7)
?
(7,-5)
?
Location
Rotation
1.
2.
To rotate the original image point (-6,-8) about the origin:
Fill in the points for a 180 degree (opposite)
and 360 degree (same as original) rotation.
Fill in the 90 and 270 degree rotations
by connecting matching coordinates.
(-6,-8)
 0            90         180        270       360
(-8,6)
?
(6,8)
?
(8,-6)
?
(-6,-8)
?
Location
Rotation
1.
2.
To rotate the original image point (-4,9) about the origin:
Fill in the points for a 180 degree (opposite)
and 360 degree (same as original) rotation.
Fill in the 90 and 270 degree rotations
by connecting matching coordinates.
(-4,9)
 0            90         180        270       360
( 9,4)
?
(4,-9)
?
(-9,-4)
?
(-4,9)
?
The End
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