Kotys Dad.............

[maverick2112]

This is a geometry assignment on investigating reflections......

Predict the image of the letter R if it is reflected across line M and then reflect the image across another line P that is parallel to M. These 2 lines can be close together or far apart just so they are parallel with each other.

1. Describe the resulting image.......My answer...(a regular R then a line..then a backwards R(the mirror of the first image)..then a line....then another regular R like the first R)......is this correct?

2. Could you have moved the original image with just one trasnformation? You should see that a translation would give you the same result? (this is how the question is worded??? My answer I would guess is yes. (Kind of confusing to me)

3.Make a conjecture about the relationship between lines of reflection and the length of the traslation vector?(again dont really know how to answer this.....

4. What happens if you reflect the omage across the far first line and then the near line? Are there cases in which the operation is commutative? My answer is that if you did the reflection this way then the backward R would be behind the far line(since you did this first) and when you reflected that image back to the near line it would be normal again. Cummutative part.....I am lost..

6. What is the result of three successive reflections?My answer.... You have your regular R then backwards(1st reflection) then normal again(2nd reflection) then backward again(3rd reflection)

This assignment doesnt seem that difficult but I am having trouble answering some questions.........

 

[KotysDad]

Re: Kotys Dad.............

Mav,

Ok, I'll give this a shot, but keep in mind that geometry is not my best subject.

1. The resulting image is the original R just moved to its new location depending on where the lines M and P are located.

2. No, not with the letter R. If you used the letter D, E, H, I, O, or X, then the answer would be yes. Those letters are symmetric across its horizontal axis, which means if you draw a horizontal line through the centers of those letters, what is above the line is identical to whats below. With those letters, any reflection yields the same letter. So you could do two reflections with one move by just putting the line of reflection in the middle of your original M and P. R is an assymetric letter, meaning you need more than 1 reflection to get back to the original.

3. Not exactly sure how detailed this answer needs to be. Short answer, the further the lines are apart, the farther away the result will be from the original position of the letter.

4. Let the near line be M and the far line be P. If you reflect across M first then P (which is what you did in #1), then you know the result. Let's assume the result of doing M and P in that order puts the resulting R "r" units away from the original. Reflecting P then M puts it "r" units away but in the opposite direction. Do a few to convince yourself paying attention to distance and direction of the resulting letter in both cases.

The commutative part of this means can you place M and P in such a way that whether you reflect M then P or P then M, both will put the resulting R in the same location. This one I am not 100% sure, but I think the only way to accomplish this is if M and P are the same line (or one on top of the other).

5. With the letter R, two reflections give you R back (in mathematical terms it has a cycle=2), So any even number of reflections gives you R back, any odd number gives you the same as if you just reflected it one time.

If you need further clarification on any of these, I may not be able to get back to you till Sunday night or Monday morning. I am taking my son down to the beach this weekend and wont be near a computer. I will check before before I leave Friday around noon. Hope this helps.

 

[dogface]

That's exactly what I was going to say but you beat me to it!

:wall: :thinking: :idea:

TSI

 

[freelancc]

That's exactly what I was going to say but you beat me to it!

:lol:

 

[maverick2112]

KD........thats plenty of help........thanks a lot I sure appreciate all the statistics,geometry and math help you have given me. It has helped a lot.

Thanks and have a great weekend............