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Which polygons are similar to Polygon A, and describe a sequence of transformations that take Polygon A to the selected polygon?

Option 1: For B, dilate with center P and a scale factor of 2, then translate 6 squares down.
Option 2: There are no similar figures to Polygon A.
Option 3: For E, rotate 90 degrees counterclockwise around S, and then translate 2 squares down and 11 squares to the right.
Option 4: All figures are similar to Polygon A.

User Nafi
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1 Answer

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Final answer:

Polygons that are similar to Polygon A can be related through a series of transformations. Option 1 using dilation and translation and Option 3 using rotation and translation both result in polygons similar to A, while Option 2 is incorrect as it denies the existence of similar polygons and Option 4 lacks specificity.

Step-by-step explanation:

You're asking which polygons are similar to Polygon A and the sequence of transformations needed to match Polygon A to the identified similar polygon. The definition of similar polygons is that they have the same shape but not necessarily the same size, and they are related by a sequence of transformations that include translations, rotations, reflections, and dilations (resizing).

For Option 1, if Polygon B is obtained from A through a dilation centered at point P with a scale factor of 2 followed by a translation of 6 squares down, then B would be similar to A. The shape of Polygon B would be the same as Polygon A but twice as large in each dimension.

Regarding Option 3, if Polygon E is obtained by rotating Polygon A 90 degrees counterclockwise around point S and then translating it 2 squares down and 11 squares to the right, Polygon E would also be similar to Polygon A. The orientation and position of E would be different but the shape would be the same.

For Option 2 and Option 4, Option 2 is incorrect because similar polygons do exist for A as explained in Options 1 and 3, while Option 4 is too broad without specific transformation instructions for each polygon. Therefore, Option 4 could be incorrect unless every figure can indeed be matched to Polygon A through the correct transformations.

User Ogbofjnr
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