Transformation Rules Flashcards

Study Notes

Rotation 90 degrees CCW about the origin: Transforms point (x,y) to (-y,x).
Rotation 180 degrees about the origin: Transforms point (x,y) to (-x,-y).
Rotation 270 degrees CCW about the origin: Transforms point (x,y) to (y,-x).
Rotation 90 degrees CW about the origin: Transforms point (x,y) to (y,-x) (same result as 270 degrees CCW).

Translation: Moves point (x,y) to (x+a,y+b), denoting a shift along the axes based on values a and b.
Reflection over the x-axis: Transforms point (x,y) to (x,-y), flipping it vertically.
Reflection over the y-axis: Transforms point (x,y) to (-x,y), flipping it horizontally.
Reflection over y = x: Transforms point (x,y) to (y,x), swapping coordinates.
Reflection over y = -x: Transforms point (x,y) to (-y,-x), flipping coordinates diagonally.

Dilation by scale factor a: Transforms point (x,y) to (ax,ay), modifying distances from the center by the scale factor.
If a > 1: The figure enlarges, increasing in size.
If a < 1: The figure reduces in size.

Transformation: General mapping of all points of a figure in a plane based on a common operation.
Reflection: A flip over a particular line to create a mirror image.
Rotation: Turning a figure about a fixed point through a specified angle and direction.
Angle of Rotation: The degree of rotation around a fixed point.

Congruent Figures: Identical in size and shape, map directly onto each other.
Similar Figures: Identical shape but different sizes; corresponding angles are congruent, and sides are proportional.
Scale Factor: The proportional relationship between corresponding lengths of two similar figures.
Corresponding Lengths: Sides in similar figures that maintain the same relative positions.
Corresponding Angles: Angles sharing the same relative position in geometric figures.

Preimage: The original figure before any transformation occurs.
Isometry: A transformation preserving both size and shape, resulting in congruent figures; often referred to as rigid transformations.