Questions and Answers
What is the translation formula (x,y) ~ ?
What does the reflection formula y=x represent?
(x,y) ~ (y,x)
How is a point reflected over the y-axis?
(x,y) ~ (-x,y)
How is a point reflected over the x-axis?
Signup and view all the answers
What is the dilation formula for a scale factor of 2?
Signup and view all the answers
What is the rotation formula for 90 degrees counterclockwise?
Signup and view all the answers
What is the rotation formula for 180 degrees?
Signup and view all the answers
What is the rotation formula for 270 degrees clockwise?
Signup and view all the answers
What does vertical reflection mean?
Signup and view all the answers
What does horizontal reflection mean?
Signup and view all the answers
What is the vertical reflection formula?
Signup and view all the answers
What is the horizontal reflection formula?
Signup and view all the answers
Study Notes
Translation
- Transformation that shifts a figure horizontally and vertically.
- Formula: (x, y) ~ (x-4, y+7) indicates a left movement of 4 units and an upward movement of 7 units.
Reflection
- Reflection over the line y = x swaps the coordinates of a point.
- Formula: (x, y) ~ (y, x).
Reflection over the y-axis
- Flips the figure over the y-axis, changing the sign of the x-coordinate.
- Formula: (x, y) ~ (-x, y).
Reflection over the x-axis
- Flips the figure over the x-axis, changing the sign of the y-coordinate.
- Formula: (x, y) ~ (x, -y).
Dilation
- A transformation that alters the size of a figure by a scale factor.
- Example: Dilation by a scale factor of 2 is represented as (x, y) ~ (2x, 2y).
Rotation 90 degrees counterclockwise
- Changes the position of a point by rotating it 90 degrees in the counterclockwise direction.
- Formula: (-y, x).
Rotation 180 degrees
- Rotates a point to the opposite quadrant.
- Formula: (-x, -y).
Rotation 270 degrees
- Rotates a point 270 degrees counterclockwise, which is equivalent to a 90-degree clockwise rotation.
- Formula: (y, -x).
Vertical reflection
- Another term for reflection over the x-axis.
- The property causes flipping across the horizontal axis.
Horizontal reflection
- Refers to reflection over the y-axis.
- The property results in flipping across the vertical axis.
Vertical reflection formula
- Represents the transformation of a function across the x-axis.
- Formula: y = -f(x).
Horizontal reflection formula
- Represents the transformation of a function across the y-axis.
- Formula: y = f(-x).
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of geometric transformations with these flashcards. This quiz covers translation, reflection, dilation, and rotation formulas with definitions and examples. Perfect for students studying geometry.
