Question

Which of these sequences 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 249° clockwise around C again
D reflect over line 1 then reflect over line 1 again

Answer 1

The sequence of transformations that would return a shape to its original position is to reflect over a line twice. therefore, option D is correct

Step-by-step explanation:

In order to return a shape to its original position, we need to perform a sequence of transformations that undoes the previous transformations. Let's analyze each sequence of transformations:

1. Sequence A: Translate 5 units right then 5 units down. This sequence of transformations does not return the shape to its original position because the shape is moved from its initial position without any reflection or rotation.
2. Sequence B: Translate 3 units down then 2 units up and then 1 unit down. This sequence of transformations does not return the shape to its original position because the shape is moved from its initial position without any rotation or reflection.
3. Sequence C: Rotate 120° counterclockwise around center C then rotate 249° clockwise around C again. This sequence of transformations does not return the shape to its original position because the total rotation angle is not a multiple of 360°.
4. Sequence D: Reflect over line 1 then reflect over line 1 again. This sequence of transformations returns the shape to its original position because reflecting over a line twice is equivalent to no reflection at all.

Therefore, the sequence of transformations that would return a shape to its original position is

Sequence D only, which is to reflect over line 1 and then reflect over line 1 again.