12.5 Transformations Review

Front

What is a translation in geometry?

Back

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

Front

How is a translation represented mathematically?

Back

A translation can be represented as (x, y) -> (x + a, y + b), where 'a' and 'b' are the distances moved in the x and y directions, respectively.

Front

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

Back

Reflecting a shape over the x-axis means that for every point (x, y) in the shape, the new point will be (x, -y).

Front

What is the rule for reflecting a shape over the y-axis?

Back

The rule for reflecting over the y-axis is (x, y) -> (-x, y).

Front

Define dilation in geometry.

Back

Dilation is a transformation that alters the size of a shape but keeps its proportions the same, defined by a scale factor.

Front

How is dilation represented mathematically?

Back

Dilation can be represented as (x, y) -> (kx, ky), where 'k' is the scale factor.

Front

What is the difference between a translation and a dilation?

Back

A translation moves a shape without changing its size or orientation, while a dilation changes the size of the shape but keeps its proportions.

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

How is a rotation represented mathematically?

Back

A rotation can be represented by specifying the angle of rotation and the center of rotation.

Front

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

Back

The effect of a 90-degree rotation counterclockwise on (x, y) is (−y, x).