anonymous
  • anonymous
How many lines of symmetry does the figure have? http://assets.openstudy.com/updates/attachments/55b90c83e4b0adef802b862b-lollygirl217-1438267354354-as.jpg Which letter has rotational symmetry? Q H G A I think it's 6 and then h and a
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
Is that right?
anonymous
  • anonymous
mathstudent55
  • mathstudent55
The question means: How many lines can you draw through the center of this figure, so that if you fold the figure in half along the line, both sides will be perfectly superimposed?

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mathstudent55
  • mathstudent55
Here is an example wit a square. |dw:1438286601391:dw| If you fold the square along that line, you get the two halves exactly on top of each other. That means that is 1 line of symmetry.
mathstudent55
  • mathstudent55
Here is another line of symmetry. |dw:1438286661309:dw|
mathstudent55
  • mathstudent55
Here are the other 2 lines of symmetry. |dw:1438286697858:dw|
mathstudent55
  • mathstudent55
A square 4 lines of symmetry.
mathstudent55
  • mathstudent55
With a regular hexagon, you have: |dw:1438286789906:dw| There are 6 different lines of symmetry.
anonymous
  • anonymous
6 lines of symatry \
anonymous
  • anonymous
nice drawing
mathstudent55
  • mathstudent55
Thanks
mathstudent55
  • mathstudent55
I don;t know about the second question bec there are no letters in your hexagon drawing.
anonymous
  • anonymous
Yay I was right on that.
anonymous
  • anonymous
@mathstudent55 it is asking which one out of those numbers has rational symmetry, it does not connect with the last connection
anonymous
  • anonymous
*question
anonymous
  • anonymous
I am guessing H and A
anonymous
  • anonymous
jk. Just H
mathstudent55
  • mathstudent55
What do the letters H and A mean? I have no idea.
mathstudent55
  • mathstudent55
Oh, I see. It means the letters themselves. It is talking about the shapes of the letters Q, H , G, and A.
mathstudent55
  • mathstudent55
Here is letter Q. If you start rotating the letter Q about its center, how much do you need to rotate (how many degrees) until the rotated shape looks like the letter Q, right side up, again? |dw:1438287423001:dw|
mathstudent55
  • mathstudent55
The answer is that you'd have to rotate Q a full 360 degrees until the little stroke of the rotated Q is on top of the original little stroke. That means the letter Q has no rotational symmetry.
mathstudent55
  • mathstudent55
What about H? |dw:1438287647869:dw|
mathstudent55
  • mathstudent55
Assuming that the capital H letter has two congruent and parallel vertical strokes positioned at the same height, and the horizontal stroke is the perpendicular bisector of the vertical strokes, then as you start rotating H about its center, when the vertical strokes become vertical again, the figure has rotated onto itself. You don't need a full 360-degree rotation for that. All you need is a 180-degree rotation. That means H has rotational symmetry.
mathstudent55
  • mathstudent55
|dw:1438287899566:dw|
mathstudent55
  • mathstudent55
Look a t the figure above. At position 1, the H is standing vertically in its normal position. It has not started to rotate yet. Then as you go to positions 2 through 6. you see the H rotating counterclockwise. When it gets to position 6, the H has rotated half a revolution, or 180 degrees. In position 6, the H looks again like an H, so the letter H does have rotational symmetry.
mathstudent55
  • mathstudent55
If you try rotating the G and the A, you will get the same result as you got with the Q. It takes a full revolution for the G and the A to look again like a proper, right side up G and A, so the G and the A, just like the Q, do not have rotational symmetry.
mathstudent55
  • mathstudent55
The answers are: 6 H
anonymous
  • anonymous
Okay, thank you.
mathstudent55
  • mathstudent55
You're welcome.

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