What set of reflections would carry rectangle abcd onto itself? rectangle abcd is shown. a is at 1, 1 and b is at 1, 3 and c is at 4, 3 and d is at 4, 1. y-axis, x-axis, y-axis x-axis, y-axis, y-axis x-axis, y=x, x-axis, y=x y=x, x-axis, y=x, y-axis

  y=x, x-axis, y=x, y-axis

Explanation:

Reflecting the figure across three axes just moves it from one quadrant to another. It does not map the figure to itself.

Reflecting across the line y=x moves it from quadrant II to IV or vice-versa. If it is in quadrant I or III, it stays there. So the sequence of reflections x-axis (moves from I to IV), y=x (moves from IV to II), x-axis (moves from II to III), y=x (stays in III) will not map the figure to itself.

However, the last selection will map the figure to itself. The initial (and final) figure location, and the intermediate reflections are shown in the attached. The figure starts and ends as blue, is reflected across y=x to green, across x-axis to orange, across y=x to red, and finally across y-axis to blue again.