Rotations

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a figure around a fixed point, called the center of rotation, by a specified angle in a specified direction.

Front

What are the coordinates of a point A(x, y) after a 180° rotation about the origin?

Back

The coordinates become A'(-x, -y).

Front

What are the coordinates of a point A(x, y) after a 90° clockwise rotation about the origin?

Back

The coordinates become A'(y, -x).

Front

What are the coordinates of a point A(x, y) after a 270° counterclockwise rotation about the origin?

Back

The coordinates become A'(-y, x).

Front

What is the image of the point S(2, -5) after a 90° clockwise rotation about the origin?

Back

S'(-5, -2).

Front

What is the image of the point W(-5, -3) after a 270° counterclockwise rotation?

Back

W'(-3, 5).

Front

How do you determine the direction of rotation?

Back

Clockwise rotation is in the direction of the hands of a clock, while counterclockwise rotation is in the opposite direction.

Front

What is the effect of a 180° rotation on a figure?

Back

A 180° rotation flips the figure to the opposite side of the center of rotation.

Front

What transformation is represented by the function (x, y) → (x + 2, y - 3)?

Back

This represents a translation, specifically sliding right 2 units and down 3 units.

Front

What is the image of the point A(3, 4) after a 180° rotation about the origin?

Back

A'(-3, -4).