Reflection of a 2-d shape about some line

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  • #1
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I've noticed the the reflection of a 2-d shape about some line is the same as rotating it by 180 degrees about that line, where it rotates through the third dimension. Does this generalise to higher dimensions? I hope it's clear what I mean here.
 
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  • #2


Yes, it generalizes exactly as you would expect. Reflecting in a plane in 3D is the same as rotating about that plane in 4D, etc.
 
  • #3


Not only that, but any rotation can be obtained by two successive reflexions, through different lines. See if you can prove that.
 

FAQ: Reflection of a 2-d shape about some line

What does it mean to reflect a 2-d shape about a line?

Reflecting a 2-d shape about a line means to create a mirror image of the shape by flipping it over the line. This results in the shape appearing identical on both sides of the line.

How is the line of reflection determined for a 2-d shape?

The line of reflection is determined by finding the perpendicular bisector of the line connecting any two corresponding points on the shape and its mirror image. This line will act as the axis of reflection.

Can any 2-d shape be reflected about any line?

Yes, any 2-d shape can be reflected about any line. The resulting image will be a mirror image of the original shape, but with all angles and distances preserved.

How does the position of the line of reflection affect the reflected shape?

The position of the line of reflection affects the orientation and location of the reflected shape. If the line is positioned closer to the original shape, the reflected image will appear larger and closer to the original. If the line is positioned further away, the reflected image will appear smaller and further away from the original.

What is the difference between reflecting a shape about a horizontal line and a vertical line?

Reflecting a shape about a horizontal line will result in the shape being flipped upside down, while reflecting about a vertical line will result in the shape being flipped from left to right. The line of reflection will also be perpendicular to the direction of the flip.

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