Transformations 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 does it mean to rotate a figure 90 degrees counterclockwise?

Back

It means to turn the figure 90 degrees in the opposite direction of the clock's hands, around a fixed point.

Front

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

Back

For a point (x, y), the new coordinates after a 90-degree counterclockwise rotation are (-y, x).

Front

What are the new coordinates of the point (3, 4) after a 180-degree rotation around the origin?

Back

The new coordinates are (-3, -4).

Front

What happens to the coordinates of a point after a 270-degree counterclockwise rotation?

Back

For a point (x, y), the new coordinates after a 270-degree counterclockwise rotation are (y, -x).

Front

If a triangle is rotated 180 degrees, how does the orientation change?

Back

The triangle will be flipped upside down, and each point will be moved to the opposite side of the center of rotation.

Front

What is the center of rotation?

Back

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

Front

How do you rotate a point (x, y) 270 degrees counterclockwise?

Back

The new coordinates will be (y, -x).

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.

Front

What are the coordinates of the point (-5, 8) after a 270-degree counterclockwise rotation?

Back

The new coordinates are (8, 5).