Question

Reflections gus reflects an object twice. the first step is to reflect it over the line y=-1. then gus completes the composite reflection by reflecting it over the line y=1. the net effect is a translation of the object. select this translation.

1) Translation 1 unit up
2) Translation 1 unit down
3) Translation 2 units up
4) Translation 2 units down

Answer 1

The object is reflected twice, with the first reflection over y=-1 and the second over y=1, resulting in a net translation 2 units up.

Step-by-step explanation:

Gus reflects an object twice for a composite transformation. The first reflection is over the line y=-1, and the second reflection is over the line y=1.

If you imagine a point above y=-1, it gets reflected to an equal distance below y=-1. When this point is then reflected over y=1, it moves upwards, again the same distance it was below y=1. The total vertical translation is therefore twice the distance between the two lines of reflection, which is 2 units (distance from y=-1 to y=1).

Thus, the net effect is a translation 2 units up, making option 3) Translation 2 units up the correct answer.