What series of transformations to quadrilateral abcd map the quadrilateral onto quadrilateral efgh to prove that abcd≅efgh ?

a reflection across x-axis, and then a translation 4 units left

a reflection across x-axis, and then a translation 4 units right

a reflection across y-axis, and then a translation 4 units right

a reflection across y-axis, and then a translation 4 units left

B:  a reflection across the x-axis followed by a translation 4 units right.

Comparing the points to their mapped images compares A to E, B to F, C to G, and D to H.  In each point, the y-coordinate switches signs and the x-coordinate is subtracted by 4.

Reflections across the x-axis will switch the sign of the y-coordinate, and reflections across the y-axis will switch the sign of the x-coordinate.  Since the y-coordinates are the ones whose sign changed, the points must have been reflected across the x-axis.

Translations to the left will cause the x-coordinate to increase, and translations to the right will case the x-coordinate to decrease.  Since the x-coordinate of every point was subtracted, this means that the translation must have been to the right.

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