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Pentagon VWXYZ is congruent to pentagon V"W"X"Y"Z". Which sequence of transformations could have been used to transform pentagon VWXYZ to produce pentagon V"W"X"Y"Z"?

A. Pentagon VWXYZ was reflected across the y-axis and then reflected across the x-axis.
B. Pentagon VWXYZ was reflected across the y-axis and then translated 2 units left and 4 units down.
C. Pentagon VWXYZ was rotated 90° counterclockwise around the origin and reflected across the y-axis.
D. Pentagon VWXYZ was translated 7 units down and then reflected across the y-axis.

Answer :

Final answer:

Given that Pentagon VWXYZ is congruent to Pentagon V"W"X"Y"Z", the feasible sequence of transformations could be - reflecting VWXYZ across the y-axis and then translating it 2 units left and 4 units down.

Explanation:

In geometry, a sequence of transformations includes operations like translations (moving a given distance in a certain direction), reflections (flipping a shape over a line), and rotations (turning a shape around a point). Given that Pentagon VWXYZ is congruent to Pentagon V"W"X"Y"Z", the transformation should preserve the shape and size of the object.

The options suggest transformations including reflections, translations, and rotations. Seeing as there is no information about changes in orientation within their individual planes, we can disregard rotations; so, among the given choices, option B – Pentagon VWXYZ was reflected across the y-axis and then translated 2 units left and 4 units down, could be a viable sequence of transformations. However, these options are based only on the information given and real solutions may vary if other transformation details were provided.

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