Chapter 11.4, Problem 19HP

To determine

To determine whether there a single transformation using reflections or translations that maps the original figure to its final image.

Answer to Problem 19HP

No, there is no single transformation

Explanation of Solution

Given:

 Reflect a figure over the $x$ -axis and then reflect it over the $y$ -axis

No, there is no single transformation using reflections or translations that maps the original figure to its final image obtained by first reflection of the image over $x$ axis and $y$ axis.

At first drawing the figure,

  

So, it’s a triangle with $xyz$ vertex.

Now drawing the reflection of the figure over $x$ -axis,

  

So, the reflected image triangle have $x\text{'}y\text{'}z\text{'}$ vertex.

Now, drawing the reflection of the figure over $y$ axis.

  

So, the final reflected image formed is having $x\text{'}\text{'}y\text{'}\text{'}z\text{'}\text{'}$ vertex.

Conclusion:

Therefore, no there is no single transformation using reflections or translations that maps the original figure to its final image.