Podcast
Questions and Answers
What is (x,y) rotated to when it undergoes a 90° CCW angle rotation around the origin?
What is (x,y) rotated to when it undergoes a 90° CCW angle rotation around the origin?
- (-x,-y)
- (x,y)
- (y,-x)
- (-y,x) (correct)
What is (x,y) rotated to when it undergoes a 90° CW angle rotation around the origin?
What is (x,y) rotated to when it undergoes a 90° CW angle rotation around the origin?
- (y,-x) (correct)
- (-x,-y)
- (x,y)
- (-y,x)
What is (x,y) rotated to when it undergoes a 180° rotation around the origin?
What is (x,y) rotated to when it undergoes a 180° rotation around the origin?
- (-x,-y) (correct)
- (-y,x)
- (x,y)
- (y,-x)
What is (4,-6) rotated 180 degrees?
What is (4,-6) rotated 180 degrees?
Rotate (4,-6) 270 degrees clockwise.
Rotate (4,-6) 270 degrees clockwise.
What does not change when you rotate a point, line, or figure?
What does not change when you rotate a point, line, or figure?
Rotating 180 degrees is the same as reflecting over what?
Rotating 180 degrees is the same as reflecting over what?
Rotating (4,-6) 90 degrees clockwise puts the point where?
Rotating (4,-6) 90 degrees clockwise puts the point where?
How many 90 degree turns would 540 degrees be?
How many 90 degree turns would 540 degrees be?
180 degree rotation about the origin results in ___.
180 degree rotation about the origin results in ___.
Flashcards
90° CCW Rotation
90° CCW Rotation
After a 90 degree counter-clockwise rotation around the origin, a point (x, y) transforms into (-y, x).
90° CW Rotation
90° CW Rotation
After a 90 degree clockwise rotation around the origin, a point (x, y) transforms into (y, -x).
180° Rotation
180° Rotation
After a 180 degree rotation around the origin, a point (x, y) transforms into (-x, -y).
Rotation Invariance
Rotation Invariance
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180° Rotation and Reflection
180° Rotation and Reflection
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270° CW = 90° CCW
270° CW = 90° CCW
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90° CW Rotation of (x,y)
90° CW Rotation of (x,y)
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Equivalent Rotations
Equivalent Rotations
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180° Rotation Result
180° Rotation Result
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180° Rotation of (4,-6)
180° Rotation of (4,-6)
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Study Notes
Rotations on the Coordinate Plane
- A 90° counterclockwise rotation of point (x,y) transforms it to (-y,x).
- A 90° clockwise rotation of point (x,y) changes it to (y,-x).
- A 180° rotation around the origin changes point (x,y) to (-x,-y).
- The point (4,-6) rotated 180 degrees around the origin results in (-4,6).
- Rotating point (4,-6) 270 degrees clockwise leads to the new position of (6,4).
- The shape or size of a point, line, or figure remains unchanged during rotation.
- A 180° rotation is equivalent to reflecting over both the x-axis and y-axis.
- When (4,-6) is rotated 90 degrees clockwise, it moves to the position (-6,-4).
- A rotation of 540 degrees equals six 90-degree rotations.
- A 180-degree rotation around the origin has the effect of flipping a shape upside down.
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Description
This quiz focuses on understanding rotations of points on the coordinate plane, specifically 90° and 180° rotations around the origin. Flashcards are provided to assist in memorizing transformations and their results. Test your knowledge of these geometric transformations effectively.
