Answer and Step-by-step explanation:
Rotating a triangle 180° using the origin as the center of rotation is equivalent to reflecting the triangle over both the x-axis and the y-axis. This can be achieved by first reflecting the triangle over the x-axis, then reflecting the resulting image over the y-axis. Neither of the given options, “a translation up 4 and then a reflection over the y-axis” nor “a translation 4 and then a translation right 6,” will produce the same result as rotating triangle ABC 180° using the origin as the center of rotation.