Rotations not at origin

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 does it mean to rotate a point about another point?

Back

To rotate a point about another point means to turn the point around the center point by a certain angle, changing its position in the coordinate plane.

Front

How do you determine the new coordinates of a point after a 90-degree clockwise rotation?

Back

For a 90-degree clockwise rotation about a point (h, k), the new coordinates (x', y') of point (x, y) are given by: (x', y') = (h + (y - k), k - (x - h)).

Front

How do you determine the new coordinates of a point after a 90-degree counter-clockwise rotation?

Back

For a 90-degree counter-clockwise rotation about a point (h, k), the new coordinates (x', y') of point (x, y) are given by: (x', y') = (h - (y - k), k + (x - h)).

Front

What is the result of rotating a point 180 degrees about another point?

Back

Rotating a point (x, y) 180 degrees about a point (h, k) results in the new coordinates (x', y') = (2h - x, 2k - y).

Front

What are the coordinates of point (5, 6) after a 90-degree clockwise rotation about (3, 3)?

Back

The new coordinates are (6, 1).

Front

What are the coordinates of point (3, 4) after a 180-degree rotation about (2, 2)?

Back

The new coordinates are (1, 0).

Front

What are the coordinates of point (2, 3) after a 90-degree clockwise rotation about (1, 1)?

Back

The new coordinates are (3, 0).

Front

What are the coordinates of point (4, 5) after a 90-degree counter-clockwise rotation about (2, 2)?

Back

The new coordinates are (-1, 4).

Front

If a point (3, 2) is rotated to (-3, -2), what is the angle of rotation?

Back

The angle of rotation is 180 degrees.