Question

0. 5*

Zach and Naomi are studying geometric transformations. Zach is able to

move the triangle A to A' using the following sequence of basic

transformations:

1. Reflection across the x-axis

2. Reflection across the y-axis

3. Translation two units to the right

864

y

A

2

ON 4

-8-6-4-20 24 68

-2-

Jö

6

-8-

A

X

Naomi claims that the same three transformations, done in any order will

always produce the same result. Zach disagrees. Who is correct?

Answer 1

Zach

Explanation:

Answer 2

Zach is correct

Explanation:

You want to know if reflection across the two axes and translation right will achieve the same effect if the transformations are done in any order.

Transformations

Translation right adds a value to the x-coordinate.

Reflection over the y-axis changes the sign of the x-coordinate.

If the order of these two transformations is changed, the result will change.

Example

Consider point (0,0) and the translation right 1 unit.

Reflection, then translation: (0, 0) ⇒ (0, 0) ⇒ (1, 0)

Translation, then reflection: (0, 0) ⇒ (1, 0) ⇒ (-1, 0)

Zach is correct that the transformations ...

1. Reflection over the x-axis
2. Reflection over the y-axis
3. Translation 2 units right

cannot be done in any order.