Transformation Formulas Flashcards

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?

What is the transformation formula for rotation 90° clockwise or 270° counterclockwise?

What is the transformation formula for rotation 180° clockwise or counterclockwise?

What is the transformation formula for rotation 270° clockwise or 90° counterclockwise?

What is the transformation formula for translation?

What is the transformation formula for dilation?

What is the result of rotating 180 degrees followed by reflecting over y = x?

What is the result of reflecting over the x-axis followed by translating up 2?

What is the result of reflecting over the x-axis followed by translating right 2?

What is the result of reflecting over y = x followed by rotating 270 degrees counterclockwise?

What is the result of dilating by 2 followed by reflecting over the y-axis?

What is the result of rotating 90 degrees clockwise followed by reflecting over the y-axis?

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).

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.