Understanding Transformations in Geometry

Front

Translation

Back

a shape without rotating or flipping

Front

Reflection

Back

a shape over a line (mirror image)

Front

Rotation

Back

a shape around a fixed point

Front

Dilation

Back

a shape larger or smaller, keeping its shape

Front

Translation rule

Back

latex="(x, y) \rightarrow (x + a, y + b)">

Front

Back

latex="(x, y) \rightarrow (x, -y)">

Front

Back

latex="(x, y) \rightarrow (-x, y)">

Front

Isometry

Back

that keeps size and shape the same

Front

Non-isometric transformation

Back

size but not shape (e.g., dilation)

Front

Preimage

Back

original figure before transformation