Your friend claims that rotating a figure by 180° is the same as reflecting a figure in the y-axis and then reflecting it in the x-axis. Is your friend correct? Explain your reasoning.

foass77W

foass77W

Answered question

2021-01-16

Your friend claims that rotating a figure by 180° is the same as reflecting a figure in the y-axis and then reflecting it in the x-axis. Is your friend correct? Explain your reasoning.

Answer & Explanation

Arnold Odonnell

Arnold Odonnell

Skilled2021-01-17Added 109 answers

Yes. Let (x,y) be a point in the original figure. Reflecting this across the y-axis, we obtain (−x,y) and reflecting the new point across the x-axis gives (−x,−y). This means that the transformation is from (x,y)(x,y) to (−x,−y) which is a rotation about the origin by 180°.

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