ROTATIONS ABOUT ANY POINT

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 does a 90° clockwise rotation do to a point (x, y)?

Back

A 90° clockwise rotation transforms the point (x, y) to (y, -x).

Front

What does a 90° anticlockwise rotation do to a point (x, y)?

Back

A 90° anticlockwise rotation transforms the point (x, y) to (-y, x).

Front

How do you determine the new coordinates after a rotation about a point (h, k)?

Back

To find the new coordinates after rotation about a point (h, k), translate the point to the origin, apply the rotation, and then translate back.

Front

What is the effect of a 180° rotation on a point (x, y)?

Back

A 180° rotation transforms the point (x, y) to (-x, -y).

Front

What is the formula for a 270° clockwise rotation?

Back

A 270° clockwise rotation transforms the point (x, y) to (-y, x).

Front

What is the formula for a 270° anticlockwise rotation?

Back

A 270° anticlockwise rotation transforms the point (x, y) to (y, -x).

Front

How do you find the coordinates of a point after a rotation of θ degrees about a point (h, k)?

Back

1. Translate the point to the origin: (x-h, y-k). 2. Apply the rotation using the rotation formulas. 3. Translate back: (new_x + h, new_y + k).

Front

What is the center of rotation?

Back

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

Front

What happens to the distance from the center of rotation after a rotation?

Back

The distance from the center of rotation to any point remains unchanged after the rotation.