Transformations

Front

What is a transformation in geometry?

Back

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

Front

What are the main types of transformations?

Back

The main types of transformations are translation, rotation, reflection, and dilation.

Front

What is a translation?

Back

A translation is a type of transformation that slides a figure horizontally, vertically, or both without changing its shape or orientation.

Front

How do you perform a translation on a point (x, y)?

Back

To translate a point (x, y) by (a, b), you add a to x and b to y, resulting in (x + a, y + b).

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 the line of reflection?

Back

The line of reflection is the line over which a figure is reflected, and each point of the original figure is equidistant from this line.

Front

How do you reflect a point (x, y) over the x-axis?

Back

To reflect a point (x, y) over the x-axis, you change the sign of the y-coordinate, resulting in (x, -y).

Front

How do you reflect a point (x, y) over the y-axis?

Back

To reflect a point (x, y) over the y-axis, you change the sign of the x-coordinate, resulting in (-x, y).

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a figure around a fixed point, known as the center of rotation, by a certain angle.

Front

What is the effect of a 90-degree rotation counterclockwise on a point (x, y)?

Back

A 90-degree rotation counterclockwise transforms the point (x, y) to (-y, x).