Question

What set of reflections and rotations would carry rectangle ABCD onto itself?

Parallelogram formed by ordered pairs A at negative 4, 1, B at negative 3, 2, C at 0, 2, D at negative 1, 1.

Rotate 180°, reflect over the x-axis, reflect over the line y=x
Reflect over the x-axis, rotate 180°, reflect over the x-axis
Rotate 180°, reflect over the y-axis, reflect over the line y=x
Reflect over the y-axis, reflect over the x-axis, rotate 180°

Answer 1

@Teddyiswatshecallsme

Answer 2

@johnweldon1993

Answer 3

@Miss.Rose

Answer 4

ok

Answer 5

its C i think good luck

Answer 6

The figure shows a parallelogram, not a rectangle.
Please check if the figure is correct.

Notwithstanding above, we first need to know each of the terms of the answer choices.
reflection about x-axis: (x, y)-> (x,-y)
reflection about y-axis: (x, y)->(-x, y)
rotation 180 degrees : (x, y)-> (-x,-y)
reflect about y=x : (x,y)-> (y, x)

Now we know A(-4,1)=(x,y)
A. Rotate 180°, (-4,1) -> (-(-4),-(1))=(4,-1)
reflect over the x-axis, (4,-1) -> (4,1)
reflect over the line y=x (4, 1) -> (1, 4)
since the final result (1,4) does not equal to original A(-4,1), therefore
A. Rotate 180°, reflect over the x-axis, reflect over the line y=x
does not map ABCD onto itself.

Continue with the other options.
Note: The correct option should have all four points A,B,C,D map back onto itself.