- 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

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- anonymous

Is that right?

- anonymous

- 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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## More answers

- 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

Here is another line of symmetry.
|dw:1438286661309:dw|

- mathstudent55

Here are the other 2 lines of symmetry.
|dw:1438286697858:dw|

- mathstudent55

A square 4 lines of symmetry.

- mathstudent55

With a regular hexagon, you have:
|dw:1438286789906:dw|
There are 6 different lines of symmetry.

- anonymous

6 lines of symatry
\

- anonymous

nice drawing

- mathstudent55

Thanks

- mathstudent55

I don;t know about the second question bec there are no letters in your hexagon drawing.

- anonymous

Yay I was right on that.

- anonymous

@mathstudent55 it is asking which one out of those numbers has rational symmetry, it does not connect with the last connection

- anonymous

*question

- anonymous

I am guessing H and A

- anonymous

jk. Just H

- mathstudent55

What do the letters H and A mean? I have no idea.

- mathstudent55

Oh, I see. It means the letters themselves. It is talking about the shapes of the letters Q, H , G, and A.

- 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

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

What about H?
|dw:1438287647869:dw|

- 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

|dw:1438287899566:dw|

- 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

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

The answers are:
6
H

- anonymous

Okay, thank you.

- mathstudent55

You're welcome.

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