Questions and Answers
What is the result of reflecting a point over the x-axis?
What is the result of reflecting a point over the y-axis?
(-x, y)
What does reflecting over the line y = x result in?
(y, x)
What is the result of reflecting a point over the line y = -x?
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What is the result of reflecting a point through the origin?
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What is the rule for a 90 degree counterclockwise rotation?
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What happens during a 180 degree rotation?
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What is the result of a 270 degree counterclockwise rotation?
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What is the rule for a 90 degree clockwise rotation?
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What is the result of a 360 degree rotation?
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What is the rule for a larger than 360 degree rotation?
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What is the rule for a 270 degree clockwise rotation?
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What is translation in terms of coordinate transformations?
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What does dilation refer to in transformations?
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What is rigid motion?
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What are the three transformations that are rigid?
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Study Notes
Reflection Rules
- Reflecting over the x-axis transforms a point (x, y) to (x, -y).
- Reflecting over the y-axis changes a point (x, y) to (-x, y).
- Reflecting over the line y = x swaps coordinates, resulting in (y, x).
- Reflecting over the line y = -x transforms the point to (-y, -x).
- Reflecting through the origin changes (x, y) to (-x, -y).
Rotation Rules
- A 90-degree counterclockwise rotation transforms (x, y) to (-y, x).
- A 180-degree rotation changes the coordinates by negating both, translating (x, y) to (-x, -y).
- A 270-degree counterclockwise rotation results in (y, -x).
- A 90-degree clockwise rotation has the same effect as a 270-degree counterclockwise rotation, yielding (y, -x).
- A 360-degree rotation leaves the point unchanged.
- For a rotation larger than 360 degrees, subtract 360 degrees from the angle to find the equivalent transformation.
- A 270-degree clockwise rotation matches a 90-degree counterclockwise rotation, transforming (x, y) to (-y, x).
Translation and Dilation Rules
- Translation involves adding or subtracting values, which results in sliding the object; it shifts a point (x, y) to (x+1, y-2).
- Dilation relates to multiplication or division, which alters the size of the object, changing (x, y) to (2x, 3y).
Rigid Motion
- Rigid motion preserves both the size and shape of the figure.
- The three transformations classified as rigid motions include reflection, translation, and rotation.
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Description
Test your knowledge of reflection and rotation rules in geometry with these flashcards. Each card presents a transformation rule with its corresponding coordinate changes. Perfect for students looking to reinforce their understanding of geometric transformations!
