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

Define translation in geometry.

Back

Translation is a transformation that moves every point of a shape the same distance in a given direction.

Front

What is a rotation?

Back

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

Front

What does reflection mean in geometry?

Back

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

Front

How do you perform a 180° rotation about the origin?

Back

To perform a 180° rotation about the origin, change the sign of both coordinates: (x, y) becomes (-x, -y).

Front

What is the effect of reflecting a point over the x-axis?

Back

Reflecting a point (x, y) over the x-axis results in the point (x, -y).

Front

Describe the transformation (x, y) → (x + 3, y - 4).

Back

This transformation is a translation 3 units to the right and 4 units down.

Front

What is the rule for a reflection over the y-axis?

Back

The rule for a reflection over the y-axis is (x, y) → (-x, y).

Front

How do you identify a rotation of 90° counterclockwise?

Back

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