Rigid Transformations

Front

What is a rigid transformation?

Back

A rigid transformation is a transformation that preserves the shape and size of a figure. The three types of rigid transformations are translations, rotations, and reflections.

Front

Define translation in geometry.

Back

Translation is a type of rigid transformation that slides a figure from one position to another without turning it. It is defined by a vector that indicates the direction and distance of the slide.

Front

What is the rule for translating a point (x, y) 4 units to the right and 3 units up?

Back

(x, y) --> (x + 4, y + 3)

Front

What does a reflection across the y-axis do to a point (x, y)?

Back

It transforms the point to (-x, y).

Front

Describe a rotation of 90 degrees clockwise around the origin for a point (x, y).

Back

The point transforms to (y, -x).

Front

What is the algebraic notation for a translation 5 units left and 2 units down?

Back

(x, y) --> (x - 5, y - 2)

Front

What is the difference between rotation and reflection?

Back

Rotation turns a figure around a fixed point, while reflection flips a figure over a line, creating a mirror image.

Front

If a figure is reflected across the line y = x, what happens to the coordinates of a point (x, y)?

Back

The coordinates switch places, transforming to (y, x).

Front

What is the effect of a dilation on a figure?

Back

Dilation changes the size of a figure but not its shape, by a scale factor.

Front

What is the rule for reflecting a point (x, y) across the line y = -2?

Back

The point transforms to (x, -4 - y).