Transformation Formulas Flashcards

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).