Rotations

Front

What is a rotation in geometry?

Back

A rotation 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 is the center of rotation?

Back

The center of rotation is the fixed point around which a figure is rotated.

Front

What is the angle of rotation?

Back

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

Front

What is the result of rotating a point (x, y) 90° counterclockwise around the origin?

Back

The result is (-y, x).

Front

What is the result of rotating a point (x, y) 180° around the origin?

Back

The result is (-x, -y).

Front

What is the result of rotating a point (x, y) 270° counterclockwise around the origin?

Back

The result is (y, -x).

Front

How do you determine the new coordinates of a point after a rotation?

Back

Use the appropriate rotation rule based on the angle of rotation and the center of rotation.

Front

What is the rule for rotating a point 90° clockwise around the origin?

Back

The rule is (x, y) → (y, -x).

Front

What is the rule for rotating a point 270° clockwise around the origin?

Back

The rule is (x, y) → (-y, x).

Front

If a triangle is rotated 90° counterclockwise, how does its orientation change?

Back

The triangle's orientation changes such that the vertices move to new positions based on the rotation rule.