standard_description: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
problem_activity: Problem 1
Describe whether the following statement is always, sometimes, or never true:
“If you reflect a figure across two parallel lines, the result can be described with a single translation rule.”
Problem 2
Describe whether the following statement is always, sometimes, or never true:
“The reflection of a figure over two unique lines of reflection can be described by a rotation.”
Problem 3
Johnny says three rotations of
$${90^{\circ}}$$
about the center of the figure is the same as three reflections with lines that pass through the center, so a figure with order 4 rotational symmetry results in a figure that also has reflectional symmetry.
Describe, using evidence from the two drawings below, to support or refute Johnny’s statement.
[IMG]


aligns: no