Question

2 describe the relationship between figures abcde and abcde using at least three math or academic vocabulary terms from the unit in your answer. underline each term you use.

Explanation:

To describe the relationship between Figures \( ABCDE \) and \( A'B'C'D'E' \), we note that a reflection over the \( y \)-axis changes the \( x \)-coordinates' signs (e.g., if a point \( (x,y) \) in \( ABCDE \), its image in the reflected figure is \( (-x,y) \)). Then, a rotation (in this case, \( 180^{\circ} \) clockwise around the origin) further transforms the figure. Since both reflection and rotation are rigid transformations, the two figures \( ABCDE \) and \( A'B'C'D'E' \) are congruent (same shape and size).

Answer:

First, we reflect \( ABCDE \) over the \( y \)-axis. Then, we rotate the reflected figure \( 180^{\circ} \) clockwise around the origin. Because reflection and rotation are rigid transformations, \( ABCDE \) and \( A'B'C'D'E' \) are congruent. The underlined terms are: reflection, rotation, rigid transformations, congruent.