Question

Triangle MNO is rotated 180 using the origin as the center of rotation .Which sequence of transformations will produce the same results?

Answer 1

The transformation of the triangle MNO will be first a reflection respect to the x-axis and second a reflection over the y-axis.

Explanation:

By definition a coordinate transformation from 180° rotation round the origen can be expressed as:

(x,y) ---> (-x,-y)

On the other hand, the coordinate transformation of the reflection over x- axis is:

(x,y) ---> (x,-y)

And the reflection over the y-axis of the this transformation is:

(x,-y) ---> (-x,-y)

That result the same transformation than the 180° rotation.

Answer 2

180° rotation about the origin changes the signs of the coordinates.

(x, y) → (-x, -y)

It is a reflection over the y-axis and a reflection over the x-axis (in either order).

You did not provide the options so hopefully you can figure out the answer based on the information I provided.