Transformations: Orientation and Congruence

Front

What is a transformation in geometry?

Back

A transformation is a function that maps a geometric figure onto a new figure, changing its position, size, or orientation.

Front

What does it mean for a transformation to preserve congruence?

Back

A transformation preserves congruence if the original figure and the transformed figure have the same size and shape.

Front

What does it mean for a transformation to preserve orientation?

Back

A transformation preserves orientation if the order of points in the figure remains the same after the transformation.

Front

What is congruence in geometry?

Back

Congruence means that two figures have the same size and shape.

Front

Give an example of a transformation that preserves congruence but not orientation.

Back

A reflection across a line preserves congruence but reverses orientation.

Front

What is the effect of a dilation transformation?

Back

A dilation transformation changes the size of a figure but keeps its shape the same.

Front

What is the difference between a rotation and a reflection?

Back

A rotation turns a figure around a point, while a reflection flips it over a line.

Front

What is the transformation notation for a translation?

Back

The notation for a translation is (x,y) → (x+a, y+b), where a and b are the horizontal and vertical shifts.

Front

What type of transformation is represented by (x,y) → (2x, 2y)?

Back

This is a dilation transformation that enlarges the figure by a scale factor of 2.

Front

What type of transformation is represented by (x,y) → (-x, y)?

Back

This is a reflection transformation that flips the figure over the y-axis.