Geometric Transformations

Vocabulary and rules covering rigid and non-rigid geometric transformations from the lecture notes.

Transformation

A rule that moves every point of a shape to a new position on a plane.

Rigid Transformation

A category of transformations that includes Translation (slide), Reflection (flip), and Rotation (turn).

Non-Rigid Transformation

A category of transformations that includes Dilation (stretch or shrink).

Translation

A change that moves all points of a figure (image) the same distance in the same direction, or slides a shape left, right, up, or down.

Reflection

Flips a shape over a line (like a mirror).

Rotation

Turns a shape around a fixed point.

Dilation

Resizes a shape larger or smaller without changing its shape.

Pre-image

The state of a shape before transformation(s) represented by points like $A$, $B$, $C$, or $D$.

Image

The state of a shape after transformation(s) represented by points like $A'$, $B'$, $C'$, or $D'$.

$$(x, y) \rightarrow (x+h, y+k)$$

The translation rule for moving a point $h$ units right and $k$ units up.

$$(x, y) \rightarrow (x+h, y-k)$$

The translation rule for moving a point $h$ units right and $k$ units down.

$$(x, y) \rightarrow (x-h, y+k)$$

The translation rule for moving a point $h$ units left and $k$ units up.

$$(x, y) \rightarrow (x-h, y-k)$$

The translation rule for moving a point $h$ units left and $k$ units down.