Transformations

Front

What is a transformation in geometry?

Back

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

Front

What are the four main types of transformations?

Back

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

Front

What is a translation?

Back

A translation moves every point of a shape the same distance in the same direction.

Front

What is a rotation?

Back

A rotation turns a shape around a fixed point, called the center of rotation, by a certain angle.

Front

What is a reflection?

Back

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

Front

What is dilation?

Back

Dilation is a transformation that changes the size of a shape but not its shape, using a scale factor.

Front

How does a translation affect the coordinates of a point?

Back

If a point (x, y) is translated by (a, b), the new coordinates will be (x + a, y + b).

Front

What happens to a shape when it is reflected over the x-axis?

Back

When reflected over the x-axis, the y-coordinates of the points change sign: (x, y) becomes (x, -y).

Front

What is the effect of a 90° clockwise rotation on the coordinates (x, y)?

Back

A 90° clockwise rotation transforms (x, y) to (y, -x).

Front

What is the effect of a 90° counterclockwise rotation on the coordinates (x, y)?

Back

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