A composition of reflections over parallel lines is the same as a __________. A. translation B. rotation C. glide reflection D. double rotation

Question

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Answer 1

A composition of reflections over parallel lines means you're taking some shape, reflecting it over a line, then reflecting it again over a line parallel to the first one.

 

When working with transformations, it's a good idea to think about whether the orientation of the shape changes for a given transformation or not. For example, a translation doesn't change the shape's orientation (< would remain <). A reflection DOES change the shape's orientation (< would become >).

 

So, the first question to ask yourself is, is this composition of reflections orientation-preserving or orientation-reversing? The first reflection will reverse the orientation (< will become >). Then, the second reflection will reverse it again (> will become <). Overall, then, this composition is orientation-preserving (< becomes > becomes <). Immediately, this tells us that the answer cannot be a glide reflection, since that would reverse orientation.

 

To figure out what IS actually going on, picture some shape in the plane and picture two vertical parallel lines to its right. Reflect the shape over the nearest parallel line, then reflect it again over the other parallel line. You'll notice that the shape winds up in the same orientation, just shifted over to the right. That's a TRANSLATION, ANSWER CHOICE A.

 

This works for any two parallel lines, not just vertical ones. Test it for yourself by drawing any shape and any two lines with the same slope. Parallel diagonal lines will translate a shape diagonally, horizontal lines will move a translate up and down, and vertical lines will translate a shape left and right.

 

 

 

If you reflected over three parallel lines, by the way, you would wind up with a simple reflection. Reflecting over two intersecting lines would create a rotation. Check this out on your own by drawing a shape and testing what happens when reflecting over various combinations of lines.

Answer 2

If we had a parallel line reflecting over one referenced parallel line, and a composition of that line reflecting over the previous line, we will have a series of repeating parallel lines reflecting over each other.  It is a never ending pattern.  If the pattern was in motion, it will look like the lines were gliding. Sort of like a flipbook.

 

Your answer is C.

Answer 3

c. a glide reflection