Transformations

Front

What is a transformation in geometry?

Back

A transformation is a mathematical operation that moves or changes a shape in some way, including translations, rotations, reflections, and dilations.

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 happens to the coordinates of a point when it is reflected over the y-axis?

Back

The x-coordinate changes sign, while the y-coordinate remains the same. For example, the point (-5, 2) becomes (5, 2).

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 (x, y) to (x + a, y + b)?

Back

You add 'a' to the x-coordinate and 'b' to the y-coordinate of each point 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, by a specified angle.

Front

What is the effect of rotating a point 90 degrees clockwise?

Back

The coordinates of the point (x, y) change to (y, -x).

Front

What is the effect of rotating a point 270 degrees counterclockwise?

Back

The coordinates of the point (x, y) change to (-y, x), which is equivalent to a 90 degrees clockwise rotation.

Front

What is a composite transformation?

Back

A composite transformation is a combination of two or more transformations applied to a figure in sequence.

Front

What does the notation R_x = 2 represent?

Back

R_x = 2 represents a reflection across the line x = 2.