The <em><u>correct answer</u></em> is:
y=x, x-axis, y=x, y-axis
Explanation:
A reflection across the line y=x maps every point (x, y) to (y, x); it switches the coordinates but does not negate them.
This means for A(1, -1), we would have A'(-1, 1); B(2, -2)→B'(-2, 2); C(3, -2)→C'(-2, 3); and D(4, -1)→D'(-1, 4).
A reflection across the x-axis negates the y-coordinate; algebraically,
(x, y)→(-x, y).
This takes our new points A'(-1, 1)→A''(-1, -1); B'(-2, 2)→B''(-2, -2); C'(-2, 3)→C''(-2, -3); and D'(-1, 4)→D''(-1, -4).
Reflecting again across the line y=x will again switch the x- and y-coordinates:
A''(-1, -1)→A'''(-1, -1); B''(-2, -2)→B'''(-2, -2); C''(-2, -3)→C'''(-3, -2); and D''(-1, -4)→D'''(-4, -1).
Reflecting across the y-axis will negate the x-coordinate:
A'''(-1, -1)→(1, -1); B'''(-2, -2)→(2, -2); C'''(-3, -2)→(3, -2); and D'''(-4, -1)→(4, -1).
These are the same as our original points.
