Geometric Transformations: Reflections, Translations, and Rotations

Vocabulary flashcards covering core geometric rules for reflections, translations, and rotations.

Reflection Across the $x$-axis

A transformation where the $y$-coordinate switches signs, mapping $(x, y)$ to $(x, -y)$.

Reflection Across the $y$-axis

A transformation where the $x$-coordinate switches signs, mapping $(x, y)$ to $(-x, y)$.

Reflection Across $x = \#$

A reflection across a vertical line located at a given value $\#$.

Reflection Across $y = \#$

A reflection across a horizontal line located at a given value $\#$.

Reflection Across $y = x$

A transformation where the $x$ and $y$ coordinates switch places, mapping $(x, y)$ to $(y, x)$.

Reflection Across $y = -x$

A transformation where the $x$ and $y$ coordinates switch places and both switch signs, mapping $(x, y)$ to $(-y, -x)$.

Translation

A rigid transformation shifting a point $(x, y)$ to $(x + h, y + k)$, where $h$ controls horizontal movement and $k$ controls vertical movement.

Horizontal Translation Rules

$x + \#$ translates a point to the Right ($R$), while $x - \#$ translates a point to the Left ($L$).

Vertical Translation Rules

$y + \#$ translates a point Up ($U$), while $y - \#$ translates a point Down ($D$).

$90^\circ$ Rotation

A rotation mapping a point $(x, y)$ to $(-y, x)$.

$180^\circ$ Rotation

A rotation mapping a point $(x, y)$ to $(-x, -y)$.

$270^\circ$ Rotation

A rotation mapping a point $(x, y)$ to $(y, -x)$.