Questions and Answers
What is the transformation formula for reflection over the x-axis?
What is the transformation formula for reflection over the y-axis?
What is the transformation formula for reflection over y = x?
What is the transformation formula for reflection over y = -x?
Signup and view all the answers
What is the transformation formula for rotation 90° clockwise or 270° counterclockwise?
Signup and view all the answers
What is the transformation formula for rotation 180° clockwise or counterclockwise?
Signup and view all the answers
What is the transformation formula for rotation 270° clockwise or 90° counterclockwise?
Signup and view all the answers
What is the transformation formula for translation?
Signup and view all the answers
What is the transformation formula for dilation?
Signup and view all the answers
What is the result of rotating 180 degrees followed by reflecting over y = x?
Signup and view all the answers
What is the result of reflecting over the x-axis followed by translating up 2?
Signup and view all the answers
What is the result of reflecting over the x-axis followed by translating right 2?
Signup and view all the answers
What is the result of reflecting over y = x followed by rotating 270 degrees counterclockwise?
Signup and view all the answers
What is the result of dilating by 2 followed by reflecting over the y-axis?
Signup and view all the answers
What is the result of rotating 90 degrees clockwise followed by reflecting over the y-axis?
Signup and view all the answers
Study Notes
Transformations Overview
- Transformations alter the position, size, or orientation of geometric figures in a coordinate plane.
Reflection Formulas
- Reflection over x-axis: Changes the y-coordinate's sign; (x,y) transforms to (x,-y).
- Reflection over y-axis: Changes the x-coordinate's sign; (x,y) transforms to (-x,y).
- Reflection over y=x: Swaps the x and y coordinates; (x,y) transforms to (y,x).
- Reflection over y=-x: Swaps and negates both coordinates; (x,y) transforms to (-y,-x).
Rotation Formulas
- 90° Clockwise: Changes the position of points by swapping coordinates and negating the new y; (x,y) transforms to (y,-x).
- 180° Clockwise (or Counter Clockwise): Inverts both coordinates; (x,y) transforms to (-x,-y).
- 270° Clockwise (or 90° Counter Clockwise): Negates the new x and swaps; (x,y) transforms to (-y,x).
Translation and Dilation
- Translation: Shifts the figure horizontally by 'a' units and vertically by 'b' units; (x,y) transforms to (x+a, y+b).
- Dilation: Changes the size of a figure; scales both coordinates by a factor 'k'; (x,y) transforms to (kx, ky).
Combined Transformations
- Rotate 180 followed by reflect over y = x: Results in coordinates (−y, −x).
- Reflect over the x-axis followed by translation up 2: Changes y-coordinates and translates upward; (x, -y+2).
- Reflect over the x-axis followed by translation right 2: Shifts right and reflects across x-axis; (x+2, -y).
- Reflect over y=x followed by rotate 270 counterclockwise: Results in (x, -y).
- Dilate by 2 followed by reflect over the y-axis: Multiplies x-coordinates by -2 and y-coordinates by 2; (−2x, 2y).
- Rotate 90 clockwise followed by reflect over the y-axis: Results in the transformation (-y, -x).
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Explore the essential transformation formulas used in geometry with these flashcards. Each card provides a specific transformation, such as reflections and rotations, along with their mathematical definitions. Ideal for students seeking to reinforce their understanding of geometric transformations.
