Question

which sequence of transformations would return a shape to its original position? a translate 5 units right, then 5 units down b translate 3 units down, then 2 units up, and then 1 unit down c rotate 120° counterclockwise around center c, then rotate 240° clockwise around c again d reflect over line l, then reflect over line l again

Explanation:

Step1: Analyze option A

Translating 5 units right and then 5 units down changes the vertical and horizontal position, won't return to original.

Step2: Analyze option B

Translate 3 units down, 2 units up and 1 unit down results in a net - 2 units down translation, won't return to original.

Step3: Analyze option C

A 120° counter - clockwise rotation and then a 240° clockwise rotation around the same center C gives a net 120° clockwise rotation, won't return to original.

Step4: Analyze option D

Reflecting a shape over a line and then reflecting it over the same line again returns the shape to its original position. Reflecting over a line is an isometry, and applying the same reflection twice is equivalent to the identity transformation.

Answer:

D. Reflect over line $\ell$, then reflect over line $\ell$ again