Transformations (Translations, Reflections, and Rotations)

Front

What is a transformation in geometry?

Back

A transformation is an operation that moves or changes a shape in some way to produce a new shape.

Front

Name the three main types of transformations.

Back

Translations, Reflections, and Rotations.

Front

What is a translation?

Back

A translation is a transformation that slides a shape from one position to another without turning or flipping it.

Front

What is a reflection?

Back

A reflection is a transformation that flips a shape over a line, creating a mirror image.

Front

What is a rotation?

Back

A rotation is a transformation that turns a shape around a fixed point at a certain angle.

Front

How do you describe a translation algebraically?

Back

A translation can be described using the rule (x, y) -> (x + a, y + b), where 'a' and 'b' are the horizontal and vertical shifts, respectively.

Front

What does the rule (x, y) -> (x + 5, y - 8) represent?

Back

This rule represents a translation of 5 units to the right and 8 units down.

Front

If a point P is at (3, 4), where will it be after a translation of (x, y) -> (x - 2, y + 3)?

Back

Point P will be at (1, 7) after the translation.

Front

What is the effect of a reflection over the x-axis on the point (x, y)?

Back

The reflection over the x-axis transforms the point (x, y) to (x, -y).

Front

What is the effect of a reflection over the y-axis on the point (x, y)?

Back

The reflection over the y-axis transforms the point (x, y) to (-x, y).