Question

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

Explanation:

Step1: Analyze translation - 1 unit left

Translation is a rigid - motion. Translating figure R 1 unit left changes its position but not its orientation or shape. Then rotating 180° clockwise around a point will not map it to figure L. So, the answer for the first sequence is No.

Step2: Analyze rotation - 180° counter - clockwise

Rotating figure R 180° counter - clockwise around the origin changes its orientation. Then translating 1 unit down does not map it to figure L. So, the answer for the second sequence is No.

Step3: Analyze reflection - across x - axis

Reflecting figure R across the x - axis flips it vertically. Then rotating the image 90° counter - clockwise around the origin does not map it to figure L. So, the answer for the third sequence is No.

Step4: Analyze rotation - 90° counter - clockwise

Rotating figure R 90° counter - clockwise around the origin changes its orientation. Then reflecting the image across the y - axis does not map it to figure L. So, the answer for the fourth sequence is No.

Answer:

No
No
No
No