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 main types are translation, rotation, and reflection.

Front

Define translation in the context of rigid transformations.

Back

Translation is a type of rigid transformation that slides a figure in a straight line from one position to another without changing its shape or size.

Front

What happens to the coordinates of a point when it is translated 3 units left and 9 units down?

Back

The new coordinates (x', y') can be found using the formula: x' = x - 3, y' = y - 9.

Front

What is rotation in rigid transformations?

Back

Rotation is a transformation that turns a figure about a fixed point (the center of rotation) by a certain angle in a specified direction.

Front

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

Back

To reflect a point (x, y) over the y-axis, the new coordinates become (-x, y).

Front

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

Back

To reflect a point (x, y) over the x-axis, the new coordinates become (x, -y).

Front

Define reflection in rigid transformations.

Back

Reflection is a transformation that flips a figure over a line (the line of reflection), creating a mirror image.

Front

What is the difference between translation and rotation?

Back

Translation moves a figure without changing its orientation, while rotation turns a figure around a point, changing its orientation.

Front

If triangle ABC is translated left 2 and up 9, what are the new coordinates of point A (x, y)?

Back

The new coordinates of point A will be (x - 2, y + 9).

Front

What is the formula for finding the new coordinates after a translation?

Back

For a translation of (a, b), the new coordinates (x', y') are given by: x' = x + a, y' = y + b.