Dilations and Rotations

Front

What is a dilation in geometry?

Back

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

Front

What does a scale factor of 2 mean in a dilation?

Back

A scale factor of 2 means that each point of the figure is moved away from the center of dilation by a distance that is twice as far as its original distance.

Front

How do you perform a dilation with the origin as the center?

Back

To perform a dilation with the origin as the center, multiply the coordinates of each point by the scale factor.

Front

What is the effect of a scale factor less than 1 in a dilation?

Back

A scale factor less than 1 reduces the size of the figure, making it smaller.

Front

What is the angle of rotation for a 90-degree clockwise rotation?

Back

A 90-degree clockwise rotation moves points in a circular direction to the right, changing their coordinates accordingly.

Front

How do you determine the new coordinates after a 180-degree rotation about the origin?

Back

For a 180-degree rotation, the new coordinates (x', y') are given by (-x, -y) for each point (x, y).

Front

What is the relationship between clockwise and counterclockwise rotations?

Back

Clockwise rotations move points in a rightward circular direction, while counterclockwise rotations move points in a leftward circular direction.

Front

What are the coordinates of point A(3, 3) after a dilation by a scale factor of 3?

Back

After dilation by a scale factor of 3, the coordinates of point A become A'(9, 9).

Front

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

Back

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

Front

How do you find the coordinates of a point after a rotation?

Back

To find the coordinates after a rotation, apply the appropriate rotation transformation formulas based on the angle of rotation.