Transformations

Front

What is a transformation in geometry?

Back

A transformation is an operation that moves or changes a shape in some way to produce a new shape.

Front

What is a translation?

Back

A translation is a type of transformation that slides a figure in a straight line from one position to another without changing its size, shape, or orientation.

Front

Describe the translation represented by (x, y) → (x-2, y+7).

Back

Translation 2 units to the left and 7 units up.

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 does it mean to reflect a figure over the x-axis?

Back

To reflect a figure over the x-axis, you change the sign of the y-coordinates of the points in the figure.

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.

Front

What does a 90-degree counterclockwise rotation do to the coordinates (x, y)?

Back

It transforms them to (-y, x).

Front

What is the image of a figure after a transformation?

Back

The image is the new figure that results from the transformation.

Front

What is the result of rotating a point (x, y) 180 degrees about the origin?

Back

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

Front

What is the difference between a rotation and a translation?

Back

A rotation turns a figure around a point, while a translation slides it without changing its orientation.