Geometric Transformations: Reflections, Rotations, and Translations

Vocabulary flashcards covering the coordinate rules and core definitions for geometric reflections, rotations, translations, and rigid motions.

Reflection across the $y\text{-axis}$

A reflection rule given by $(x, y) \rightarrow (-x, y)$, where the $x$-coordinate becomes its opposite and the $y$-coordinate stays the same.

Reflection across the $x\text{-axis}$

A reflection rule given by $(x, y) \rightarrow (x, -y)$, where the $x$-coordinate stays the same and the $y$-coordinate becomes its opposite.

Reflection across the line $y = x$

A reflection rule given by $(x, y) \rightarrow (y, x)$, where the $x$ and $y$ coordinates switch positions.

Reflection across the line $y = -x$

A reflection rule given by $(x, y) \rightarrow (-y, -x)$, where the coordinates swap positions and both become their opposites.

Negative sign in transformation rules

A symbol in coordinate notation indicating "the opposite" of that coordinate value.

Rotation of $90^\circ$

A counter-clockwise rotation rule given by $(x, y) \rightarrow (-y, x)$, where $y$ becomes the opposite and $x$ stays the same.

Rotation of $180^\circ$

A rotation rule given by $(x, y) \rightarrow (-x, -y)$, where both $x$ and $y$ become their opposites.

Rotation of $270^\circ$

A counter-clockwise rotation rule given by $(x, y) \rightarrow (y, -x)$, where $y$ stays the same and $x$ becomes the opposite.

Rigid motion

A transformation that preserves length and angle measures.

Pre-image

The original figure prior to a transformation, denoted in the notes as $ABC$.

Image

The resulting figure after a transformation is applied, denoted in the notes as $$A'B'C'$.