The set of reflections that would carry rectangle ABCD back to itself is: <span>y-axis, x-axis, y-axis, x-axis. </span> By reflecting the original image over y-axis, the transformed image moves to the 1st quadrant of the cartesian plane. By reflecting the image in quadtrant 1 over x-axis, the image moves to the 4th quadrant, and by reflecting it again over y-axis and another over the x-axis, it goes back to its original position in the 2nd quadrant.
Reflection about the y-axis has rule (x,y)→(-x,y);
Reflection about the x-axis has rule: (x,y)→(x,-y).
Consider rectangle ABCD and select, for example point A(-5,1).The set of reflections about the y-axis, x-axis, y-axis, x-axis will act on A in following way:
about y-axis A(-5,1)→A'(5,1);
about x-axis A'(5,1)→A''(5,-1);
about y-axis A''(5,-1)→A'''(-5,-1);
about x-axis A'''(-5,-1)→A(-5,1).
This reflections act on all rectangle vertices in the same way, then
the set of reflections that carry rectangle ABCD onto itself is
