High School Geometry

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Darin Marsh

December 31, 2018 11:03

Can someone help me understand how to answer this question? I feel like circle O can be transformed to O1 via reflection, rotation or translation. Based on the property given I don’t know how to choose a distinct transformation.

Question:
A certain mapping in the xy-plane has the following property:

Each circle O with radius r and centered at (x,y) is mapped to circle O1 with radius r and centered at (x + 11,y -7).

Choose 1 answer:

A - the property defines a reflection
B - the property defines a rotation
C - the property defines a translation

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Regina Litman

January 01, 2019 17:54
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Unconditionally, this is a translation because you don’t need a particular line through which to reflect it or a particular point to serve as a center of rotation. All you need is to move it 11 units to the right and then 7 units down.

You ccould reflect it through a carefully placed line that passes through (x+5.5,y-3.5) and whose slope is -7/11, but this mapping only works for this particular situation.

You could rotate it 180 degrees around the point (x+5.5,y-3.5) and possibly other degree measurements around other points along the line 11x-7y=36, but again, these mappings only work for those particular situations.

Thus, the correct answer for every case is C.

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High School Geometry

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