Transformations Review

Front

What is a translation in geometry?

Back

A translation is a transformation that moves every point of a shape a constant distance in a specified direction.

Front

How do you represent a translation mathematically?

Back

A translation can be represented by a vector, such as (x + a, y + b), where (a, b) is the vector indicating the direction and distance of the translation.

Front

What is the result of translating a point (x, y) by the vector (2, -3)?

Back

The new coordinates will be (x + 2, y - 3).

Front

What is a reflection in geometry?

Back

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

Front

How do you reflect a point (x, y) over the line y = x?

Back

To reflect a point over the line y = x, you swap the coordinates, resulting in (y, x).

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a shape around a fixed point, known as the center of rotation.

Front

What does a 90° counterclockwise rotation do to a point (x, y)?

Back

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

Front

What is the effect of a 180° rotation about the origin on a point (x, y)?

Back

A 180° rotation about the origin transforms the point (x, y) to (-x, -y).

Front

What is the formula for translating a point by a vector (a, b)?

Back

The formula is (x, y) -> (x + a, y + b).

Front

How do you find the image of a point after a translation?

Back

To find the image of a point after a translation, add the translation vector to the original coordinates.