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41 votes
41 votes
Select all of the sequences of transformations that would return a shape to its original position.

Translate 3 units up, then 3 units down.

Translate 3 units up, then 3 units down.


Reflect over the y axis, then reflect over the y axis again.

, , Reflect over the y axis, then reflect over the y axis again. ,

Translate 1 unit to the right, then 4 units to the left, then 3 units to the right.

Translate 1 unit to the right, then 4 units to the left, then 3 units to the right.


Rotate 120º counterclockwise around center , then rotate 90º counterclockwise around again.

User Archaelus
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1 Answer

16 votes
16 votes

Answer:

Except d. Rotate 120 degrees around center c then rotate 220 degrees around again.

Explanation:

For a. Translate 3 units up, then 3 units down is easy to see that this will return the square to its original position. Wherever we translate up and then down the same units a particularly shape this will return to its original position.

For b. Reflect over line p, then reflect over line p again

Wherever we have any particularly shape and we reflect over an arbitrary line twice, the shape will return to its original position. Particularly, the composition of two reflections over the same line is the identity function.

The identity function is the function that doesn't change the shape (It is the analogy of the multiplication by 1 with the common product between real numbers).

c. Translate 1 unit to the right, then 4 units to the left, then 3 units to the right.

The composition of this three translation will return the square to its original position (Same reasoning as a.)

d. Rotate 120 degrees around center c then rotate 220 degrees around c again.

Given that we choose an arbitrary center c and then chosen an arbitrary rotation sense (counterclockwise or clockwise), the composition of the two rotations is a 340 degrees rotation (given that we sum the degrees).

This transformation will not return a shape to its original position

(Of course, it exists some exceptions such as a rotation of a circle around its center. For any value of degrees, the rotation of a circle around its center will return the circle to its original position).

Generally, option d. is the correct option.

User Jan Hudec
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3.0k points
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