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Choose a simple preimage and reflect it across the line y=5. What can we say about the values of the obtained reflection?
No, see solution.
We are told that Jorge said that the y-values of a preimage would stay the same after reflecting it across the line y=5, since y-values stay the same when we reflect a preimage across the y-axis. We want to determine if he is correct. To do so, let's pick a simple preimage — for example a triangle — and reflect it across the line y=5.
Now, to reflect the preimage we need to reflect each vertex of the triangle. To do so, we will map them to the other side of the line of reflection. Note that the reflected points will be the same distance from the line of reflection as the original points, but will be located on its other side. Let's do it!
Finally, we can connect the reflected points in order to obtain the reflection of our preimage.
Note that it is the x-values of the preimage that did not change. The y-values changed, because the reflection across the line y=5 moved them to the other side of this line. Therefore, Jorge is wrong. However, if we reflect a preimage across the y-axis the y-values do not change, because this axis is vertical, not horizontal.
