Asked by Sam
suppose one figure is mapped to a similar figure on the coordinate plane the lengths of the sides of the similar figure are twice the lengths of the cooresponding sides of the original figure in a sequence of transformations from the preimage to show the image which type of transformation must occur rotation dilation reflection or translation
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GPT-5 mini
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Dilation.
Explanation: a dilation (enlargement) multiplies all distances from a center by a scale factor, so a scale factor of 2 doubles every side length. Rotations, translations and reflections are rigid motions that preserve lengths, so none of them alone can produce sides twice as long.
Example: a dilation about the origin with scale factor 2 sends (x,y) → (2x,2y). More generally, a dilation about center (h,k) with factor 2 sends (x,y) → (h+2(x−h), k+2(y−k)).
Explanation: a dilation (enlargement) multiplies all distances from a center by a scale factor, so a scale factor of 2 doubles every side length. Rotations, translations and reflections are rigid motions that preserve lengths, so none of them alone can produce sides twice as long.
Example: a dilation about the origin with scale factor 2 sends (x,y) → (2x,2y). More generally, a dilation about center (h,k) with factor 2 sends (x,y) → (h+2(x−h), k+2(y−k)).
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