What is the transformation that flips a shape over a given point and is equivalent to a 180-degree rotation around that point?

A transformation that flips a shape over a given point, resulting in an arrangement that is equivalent to a 180-degree rotation around that point, is known as point reflection. This specific type of reflection entails that each point of the shape is moved directly to the opposite side of the defined point, ensuring that the original shape and its reflected shape are symmetrical with respect to that point.

For instance, if you have a shape and you take a point located at its center and reflect every point of the shape through this center point, the resulting shape will be a mirrored version, precisely positioned as if it had been rotated by 180 degrees around that center point. This is different from line reflection, which reflects points across a line, and rotation, which involves spinning the shape around a certain point without the mirroring effect. Glide reflection involves both a line reflection and a translation, which further differentiates it from point reflection. Thus, point reflection is the transformation that precisely fits the description provided in the question.