Embedded Files
Rotations
Rotations
Standard
G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
Goals for this section:
Goals for this section:
To understand that rotations will generally go in the counterclockwise direction unless specified and that in this class, we'll generally go 90, 180, or 270 degrees.
This notation means: the rotation going x° counterclockwise of UVW about the point Q is U'V'W'
This notation means: the rotation going x° counterclockwise of UVW about the point Q is U'V'W'
- r stands for rotation
- x° how much you'll rotate
- Q is where you're rotating around
Rotating 90°, 180°, and 270° counterclockwise about the origin
Rotating 90°, 180°, and 270° counterclockwise about the origin
r(90°,O)(x,y)=(-y,x)
This is how to apply a 90° rotation about the origin which is O.
- Notice how the lines make a 90° angle about the origin.
- (1,2) is what we're rotating.
- Take the y-value, 2, change its sign, and put it in the first spot like this (-2,_).
- Now take the x-value, 1, and put it in the second spot like this (-2, 1).
r(180°,O)(x,y)=(-x,-y)
This is how to apply a 180° rotation about the origin which is O.
- Notice how the lines make a 180° angle about the origin.
- (1,2) is what we're rotating.
- Take the x-value, 1, and change the sign. Our coordinate will look like (-1,_).
- Take the y-value, 2, and change the sign. Our coordinate will be (-1, -2).
r(270°,O)(x,y)=(y,-x)
This is how to apply a 270° rotation about the origin which is O.
- Notice how the lines make a 270° angle about the origin.
- (1,2) is what we're rotating.
- Take the y-value, 2, and put it in the first spot like this (2,_).
- Take the x-value, 1, change the sign and put it in the second spot like this (2, -1).
Rotating Clockwise
Rotating Clockwise
Rotating clockwise is the same as counterclockwise
Rotating clockwise is the same as counterclockwise
So notice how if you're asked to rotate clockwise 270°, it's the same as rotating counterclockwise 90°.
So notice how if you're asked to rotate clockwise 270°, it's the same as rotating counterclockwise 90°.
Similarly,
- Rotating clockwise 180° is the same as rotating counterclockwise 180°.
- Rotating clockwise 90° is the same as rotating counterclockwise 270°
Keywords: rotations, 90, 180, 270, counterclockwise, clockwise
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