Transformations

Front

What is a transformation in geometry?

Back

A transformation is a mathematical operation that moves or changes a shape in some way, such as translation, rotation, reflection, or dilation.

Front

What is a translation?

Back

A translation is a type of transformation that slides a figure from one position to another without turning it.

Front

What is a rotation?

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 a reflection?

Back

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

Front

What is the coordinate rule for reflecting over the x-axis?

Back

To reflect a point (x, y) over the x-axis, the new coordinates become (x, -y).

Front

What is the coordinate rule for reflecting over the y-axis?

Back

To reflect a point (x, y) over the y-axis, the new coordinates become (-x, y).

Front

What is the coordinate rule for a 90-degree clockwise rotation?

Back

To rotate a point (x, y) 90 degrees clockwise, the new coordinates become (y, -x).

Front

What is the coordinate rule for a 90-degree counterclockwise rotation?

Back

To rotate a point (x, y) 90 degrees counterclockwise, the new coordinates become (-y, x).

Front

What is the coordinate rule for a 180-degree rotation?

Back

To rotate a point (x, y) 180 degrees, the new coordinates become (-x, -y).

Front

How do you determine the type of transformation from coordinates?

Back

By comparing the original and transformed coordinates, you can identify the type of transformation (translation, rotation, reflection) based on the changes in the coordinates.