Rotations and Dilations

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a figure around a fixed point, called the center of rotation, by a certain angle in a specific direction.

Front

What is a dilation in geometry?

Back

A dilation is a transformation that changes the size of a figure but not its shape, using a center of dilation and a scale factor.

Front

What does the scale factor in a dilation represent?

Back

The scale factor indicates how much larger or smaller the figure will be after the dilation. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

If point A (4, 6) is dilated with a scale factor of 1/2, what are the new coordinates?

Back

(2, 3)

Front

What happens to the coordinates of a point when it is rotated 90° counterclockwise around the origin?

Back

The new coordinates (x', y') are given by (-y, x).

Front

If a point is in quadrant 3, where will it be after a 90° counterclockwise rotation?

Back

It will move to quadrant 2.

Front

What is the symbol used to denote new vertices after a transformation?

Back

The symbol ' (prime) is used to denote new vertices after a transformation.

Front

How do you determine the quadrant of a point given its coordinates?

Back

The quadrant can be determined by the signs of the x and y coordinates: Quadrant I (x>0, y>0), Quadrant II (x<0, y>0), Quadrant III (x<0, y<0), Quadrant IV (x>0, y<0).

Front

What are the coordinates of point B after a dilation with center (0,0) and scale factor 3 if B is at (1,2)?

Back

(3, 6)

Front

What is the effect of a dilation with a scale factor of 1 on a figure?

Back

The figure remains unchanged in size and shape.