Question

if pentagon abcd was reflected over the axis y-axis, reflected over the x-axis, and rotated 180, where would be point A' lie

Answer 1

A reflection over the x axis coupled with another reflection over the y axis leads to a rotation of 180 degrees. 

In other words,

Start with point A. Reflect over the x axis to get point B. Reflect B over the y axis to get point C. To go from A to C, we can rotate A 180 degrees about the origin.

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So this means that if we do those reflections and then do the rotation, then we end up back where we started. Wherever point A is located, the point A' will also be located at the same position with the same coordinates.