Subjects geometry

Circle Transformation Error

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Circle Transformation Error


1. The problem is to identify the error Pedro made in concluding whether circle A can be mapped onto circle B by geometric transformations. 2. Circles are all similar because they can be mapped onto each other by a dilation (scaling), regardless of rotation or translation. 3. Rotation or translation alone cannot change the size of a circle, thus they cannot make two circles of different sizes coincide. 4. Pedro concluded that one more transformation (a rotation) would map circle A onto circle B, implying similarity. This is incorrect because rotation does not change size. 5. The correct transformation to make circle A map onto circle B is a dilation (scaling) which changes the size but preserves shape. 6. Therefore, the error is that Pedro assumed a rotation suffices instead of a dilation. Final answer: B One more transformation — a dilation — would map circle A onto circle B. So the circles are similar.