Explore Rotations in Geometry

Front

What is a rotation in geometry?

Back

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

Front

What happens to the coordinates of a point (x, y) when it is rotated 180 degrees around the origin?

Back

The coordinates change to (-x, -y).

Front

How do you determine the angle of rotation for a figure?

Back

The angle of rotation is the measure of the degree through which the figure is turned around the center of rotation.

Front

What is the result of rotating a point (a, b) 90 degrees clockwise around the origin?

Back

The new coordinates will be (b, -a).

Front

What is the result of rotating a point (a, b) 90 degrees counterclockwise around the origin?

Back

The new coordinates will be (-b, a).

Front

If a figure is rotated 270 degrees clockwise, what is the equivalent counterclockwise rotation?

Back

The equivalent counterclockwise rotation is 90 degrees.

Front

What is the image of the point (2, 3) after a 180-degree rotation around the origin?

Back

The image of the point will be (-2, -3).

Front

How can you visualize a rotation transformation?

Back

You can visualize a rotation transformation by imagining the figure spinning around a point, maintaining its shape and size.

Front

What is the difference between clockwise and counterclockwise rotation?

Back

Clockwise rotation moves in the same direction as the hands of a clock, while counterclockwise rotation moves in the opposite direction.

Front

What is the effect of a 360-degree rotation on a figure?

Back

A 360-degree rotation returns the figure to its original position.