Geometric Transformations

Vocabulary and coordinate rules for translations, reflections, and rotations on a coordinate plane.

Translation

A transformation characterized as a slide.

Translation to the right

A coordinate shift given by the rule $(x, y) \rightarrow (x + \#, y)$.

Translation to the left

A coordinate shift given by the rule $(x, y) \rightarrow (x - \#, y)$.

Translation up

A coordinate shift given by the rule $(x, y) \rightarrow (x, y + \#)$.

Translation down

A coordinate shift given by the rule $(x, y) \rightarrow (x, y - \#)$.

Reflection

A transformation characterized as a flip.

Reflection across the x-axis

A reflection given by the rule $(x, y) \rightarrow (x, -y)$.

Reflection across the y-axis

A reflection given by the rule $(x, y) \rightarrow (-x, y)$.

Reflection across the line $y = x$

A reflection given by the rule $(x, y) \rightarrow (y, x)$.

Reflection across the line $y = -x$

A reflection given by the rule $(x, y) \rightarrow (-y, -x)$.

Rotation

A transformation characterized as a turn.

$90^\circ$ Counterclockwise / $270^\circ$ Clockwise Rotation

A rotation rule given by $(x, y) \rightarrow (-y, x)$.

$270^\circ$ Counterclockwise / $90^\circ$ Clockwise Rotation

A rotation rule given by $(x, y) \rightarrow (y, -x)$.

$180^\circ$ Rotation

A rotation rule given by $(x, y) \rightarrow (-x, -y)$.