Question

figures r and l are shown on the coordinate grid. (a) determine whether each sequence of transformations shows that figure r is congruent to figure l. select yes or no for each sequence of transformations. (b) translate figure r 1 unit left. then rotate the image 180° clockwise. (c) rotate figure r 180°. then counterclockwise around the origin. then translate the image 1 unit down. (d) reflect figure r across the x - axis. then rotate the image 90°. then counterclockwise around the origin. (e) rotate figure r 90°. then counterclockwise around the origin. then reflect the image across the y - axis.

Explanation:

Step1: Recall congruence - transformation rules

Congruent figures have the same shape and size. Transformations like translations, rotations, and reflections preserve congruence.

Step2: Analyze each transformation sequence

• For the first sequence (translate 1 unit left then rotate 180° clockwise): A translation is a rigid - motion that just moves the figure and a 180° rotation is also a rigid - motion. So, it preserves congruence.
• For the second sequence (rotate 180° counter - clockwise around the origin then translate 1 unit down): Rotation and translation are rigid motions, so it preserves congruence.
• For the third sequence (reflect figure R across the x - axis then rotate the image 90° counter - clockwise around the origin): Reflection and rotation are rigid motions, so it preserves congruence.
• For the fourth sequence (rotate figure R 90° counter - clockwise around the origin then reflect the image across the y - axis): Rotation and reflection are rigid motions, so it preserves congruence.

Answer:

Yes, Yes, Yes, Yes