Transformations review

Front

What are transformations in geometry?

Back

Transformations are operations that alter the position, size, or shape of a figure. Common types include translations, rotations, reflections, and dilations.

Front

What is a translation in geometry?

Back

A translation is a transformation that moves every point of a figure the same distance in a specified direction.

Front

How do you perform a translation of a point?

Back

To translate a point (x, y) by (a, b), add a to the x-coordinate and b to the y-coordinate: (x, y) → (x + a, y + b).

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.

Front

What is the rule for a 90° counterclockwise rotation?

Back

The rule for a 90° counterclockwise rotation around the origin is (x, y) → (-y, x).

Front

What is a reflection in geometry?

Back

A reflection is a transformation that flips a figure over a line, creating a mirror image.

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 scale factor.

Front

How do you perform a dilation with a scale factor of k?

Back

To dilate a point (x, y) by a scale factor of k, multiply both coordinates by k: (x, y) → (kx, ky).

Front

What is the scale factor in a dilation?

Back

The scale factor is a number that describes how much a figure is enlarged or reduced during a dilation.

Front

What are the coordinates of point D if it is at (-3, -3)?

Back

The coordinates of point D are (-3, -3).