Sequences of Transformations

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

Define translation in the context of transformations.

Back

Translation is a transformation that moves every point of a shape the same distance in the same direction.

Front

What is a reflection in geometry?

Back

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

Front

Explain what a rotation is in geometric transformations.

Back

Rotation is a transformation that turns a shape around a fixed point, called the center of rotation, by a certain angle.

Front

What does 180° rotation mean?

Back

A 180° rotation means turning a shape halfway around a circle, resulting in a shape that is upside down.

Front

What is the effect of a 90° counterclockwise rotation on a point (x, y)?

Back

The point (x, y) becomes (-y, x) after a 90° counterclockwise rotation.

Front

What happens to a point (x, y) during a 90° clockwise rotation?

Back

The point (x, y) becomes (y, -x) after a 90° clockwise rotation.

Front

Define reflection over the x-axis.

Back

Reflection over the x-axis means that for any point (x, y), the new point will be (x, -y).

Front

What is reflection over the y-axis?

Back

Reflection over the y-axis means that for any point (x, y), the new point will be (-x, y).

Front

Explain reflection over the line y = x.

Back

Reflection over the line y = x means that for any point (x, y), the new point will be (y, x).