Question

What reflection, or composition of reflections, always produces the same image as a rotation 180 degrees about the origin? a A reflection over the x-axis followed by a reflection of that image over the x-axis. b A reflection over a line that bisects the figure. c A reflection over the x-axis followed by a reflection of that image over the y-axis. d A reflection over the line y = x.

Answer 1

C is the answer because of the rules of rotation and reflection. If you don't know these rules you may ask.

Answer 2

Answer: The correct option is C

Explanation:

A reflection over the x-axis followed by a reflection of that image over the y-axis

Some polygons have rotational symmetry, some have reflectional symmetry. If you rotate an object by 180 degrees, or reflect it in a suitable axis, you get back the same shape.

If you rotate a shape by 180 degrees, you get an upside down shape, not a reflected shape.

Do the reflection in x-axis followed by the reflection in the y-axis. You will discover that your new image will land on top of the original image.

Option d can only work if y = -x