Transformations

Front

What are transformations in geometry?

Back

Transformations are operations that alter the position, size, or shape of a figure in a geometric space.

Front

What are the three main types of transformations?

Back

Translations, reflections, and rotations.

Front

What is a translation?

Back

A translation is a transformation that slides a figure from one position to another without turning it.

Front

What is a reflection?

Back

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

Front

What is a rotation?

Back

A rotation is a transformation that turns a figure around a fixed point at a certain angle.

Front

How do you reflect a point over the y-axis?

Back

To reflect a point (x, y) over the y-axis, change the sign of the x-coordinate: (-x, y).

Front

How do you reflect a point over the x-axis?

Back

To reflect a point (x, y) over the x-axis, change the sign of the y-coordinate: (x, -y).

Front

What is the rule for translating a point 2 units left and 3 units up?

Back

The rule is (x, y) → (x - 2, y + 3).

Front

What does the transformation (x, y) → (x + 2, y - 3) represent?

Back

It represents a translation 2 units to the right and 3 units down.

Front

What is the result of reflecting the point (2, -4) over the y-axis?

Back

The result is (-2, -4).