SOLUTION: Matt wants to reflect a shape over the x-axis and then reflect it over the y-axis. Cathy says that this would be the same as rotating the shape 180 degrees. Do you agree or disagre

Question 1123182: Matt wants to reflect a shape over the x-axis and then reflect it over the y-axis. Cathy says that this would be the same as rotating the shape 180 degrees. Do you agree or disagree with Cathy? Justify your answer and use matrix transformations as part of your justification.
thanks for any help!!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe that would be correct.

even though rotating 90 degrees is not the same as reflecting about the y-axis,when you reflect again about the x-axis, it becomes the same as reflecting an additional 90 degrees.

so reflecting about the y and then about the x is the same as rotating 180 degrees.

what happens when you rotate 180 degrees is that (x,y) becomes (-x,-y)

when you reflect about the y-axis, (x,y) becomes (-x,y).

when you reflect again about the x-axis, (-x,y) becomes (-x,-y).

you can see this using an example of the point (7.3) in the following display.

the following example shows what happens.

rotating 90 degrees is not the same as reflecting about the y-axis, but when you reflect that about the x-axis, the original symmetry is restored.

in the example, you can see tht rotqting 90 degrees moves the point from (7,3) to (-3,7).

rotating another 90 degrees moves the point from (-3,7) to (-7,3).

reflecting about the y-axis moves the point from (7,3) to (-7,3).

reflecting again about the x-axis moves the poijnt from (-7,3) to (-7,-3).

the end result is that the point winds up in the same spot whether you rotated 180 degrees or whether you reflected about the y and then the x axis.

$$$

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