SECTION 7.6ROTATIONS AND ROTATIONALSYMMETRY
ROTATIONS
There are two types of rotations:
CW – Clockwise
CCW – Counter Clockwise
Objects are usually rotated around the followingangles: 90, 180, 270
CW
CCW
Quarter Circle:
Half Circle:
3 Quarters Circle
Full Circle:
WINDMILL METHOD:
When asked to rotate a point about the origin by 90, 180,or 270 degrees create a windmill using the X and Y axis
ie: rotate the point (3,4) about the origin by 90°, 180°, &270°cw
With the windmill, we can find the coordinates of thepoint after the rotation
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
1
2
3
4
5
Practice: Given the point P(-2,4)
i) Rotate it 90° ccw about the origin
ii) Rotate it 180° ccw about the point (1,1)
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
1
2
3
4
5
EX: GIVEN THE FOLLOWING OBJECT, ROTATE IT 90⁰ (CW) ABOUTTHE ORIGIN AND FIND THE COORDINATES OF THE VERTICES:
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
1
2
3
4
5
When the object is rotated90°, objects pointing upwill point to the right
After you rotate the objectfind the coordinates ofeach vertex
PRACTICE: GIVEN THE FOLLOWING OBJECTS, FIND THECOORDINATES OF THE VERTEX AFTER EACH ROTATION:
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
1
2
3
4
5
180 degree CW rotation about the origin
90 degree CCW rotation about point “I”
ROTATIONAL SYMMETRY
Objects can be rotated such that it will look the same
A square has rotational symmetry because you canrotate it 90 degrees and look the same
Order of rotation: How many different angles it can berotated so that it looks the same
Angles need to be less than or equal to 360 degrees
Q: How many order of rotations does a square have?
4 order of operation
90 degrees
180 degrees
270 degrees
360 degrees
EX: WHICH OF THE FOLLOWING HAVE ROTATIONALSYMMETRY? IF YES, INDICATE THE ORDER OF ROTATION:
5 order of operation
3 order of operation
2 order of operation
7 order of operation
1 order of operation
4 order of operation
HOMEWORK:
P366 # 4 – 6, 8 – 10, 13 – 14