Transcript Honors Geometry Transformations Section 2 Rotations

Honors Geometry Transformations
Section 2
Rotations
A rotation is a transformation in
which every point is rotated the
same angle measure around a fixed
point.
The fixed point is called the
center of rotation.
The ray drawn from the center of
rotation to a point and the ray
drawn from the center of rotation
to the point’s image form an
angle called the angle of rotation.
angle of
rotation
center of rotation
Rotations
can be clockwise ( ) or
counterclockwise ( ).
Let’s take a look at rotations in the
coordinate plane.
Example 1: Rotate A B 180 clockwise
about the origin (0, 0).
Give the coordinates of
(0,  6)
A  _______
  1,  2 
B  _______
Would the coordinates of A  and
B  be different if we had
rotated counterclockwise instead?
NO
Rotations around the origin can be
made very easily by simply rotating
your paper the required angle
measure.
Note: The horizontal axis is always
the x-axis and the vertical axis is
always the y-axis.
Example 2: Rotate A B 90 clockwise
about the origin.
Give the coordinates of
A  ________
B  ________
Example 2: Rotate A B 90 clockwise
about the origin.
Give the coordinates of
6,
0


________

A
2,

1


________
B
A
B
Example 3: Rotate A B 90
counterclockwise about the origin.
Give the coordinates of

6,
0


________

A

2,1


________
B
B
A
For rotations of 900 around a point
other than the origin, we must
work with the slopes of the rays
forming the angle of rotation.
Remember: If two rays are
perpendicular then their slopes are
opposite reciprocals.
Example 4: Rotate A B 90
clockwise about the point (–1, 3).
opposite reciprocal 
-1

3
1
3
3
1
opposite reciprocal 
2
1

2
1
1
2
B
A
Example 4: Rotate A B 90
counterclockwise about the point (–1, 3).
opposite reciprocal 
-1

3
1
3
A
opposite reciprocal 
2
1

2
1

B
3
1
1
2
Example 6: Rotate A B 900
counterclockwise around the point (3, 0)
opposite reciprocal 
3

6
3
6
6
3
opposite reciprocal 
2
2

2
2
2
2
A
B
A figure has rotational symmetry if
it can be rotated through an angle
of less than 360 and match up with
itself exactly.
Example 7: State the rotational
symmetries of a
square
regular pentagon
90 , 180, 270
72 ,144 , 216 , 288
Example 8: Name two capital
letters that have 180 rotational
symmetry.
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