Transformations: Reflections, Translations, 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

What are the three main types of transformations?

Back

Reflections, Translations, and Rotations.

Front

Define reflection in geometry.

Back

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

Front

What is the rule for reflecting a point (x, y) over the x-axis?

Back

(x, y) → (x, -y).

Front

What is the rule for reflecting a point (x, y) over the y-axis?

Back

(x, y) → (-x, y).

Front

What is a translation in geometry?

Back

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

Front

What is the rule for translating a point (x, y) by (a, b)?

Back

(x, y) → (x + a, y + b).

Front

Define rotation in geometry.

Back

A rotation is a transformation that turns a figure around a fixed point, called the center of rotation.

Front

What is the rule for rotating a point (x, y) 90 degrees counterclockwise around the origin?

Back

(x, y) → (-y, x).

Front

What is the rule for rotating a point (x, y) 180 degrees around the origin?

Back

(x, y) → (-x, -y).