Which statement is an example of a transformation in geometry?

The statement that involves shifting a point to another location on the graph is an example of a transformation in geometry because it describes a specific action that changes the position of an object in a coordinate system. Transformations involve altering the position, size, orientation, or shape of geometric figures, and shifting a point signifies a translation, which is one of the fundamental types of transformations along with rotations, reflections, and dilations.

In contrast, doubling the size of a shape symbolizes a type of transformation as well, specifically dilation, but it refers to rescaling rather than repositioning. On the other hand, finding the area of a triangle and measuring angles in a polygon do not involve a transformation; they are operations performed on geometric figures but do not change their spatial configuration. Thus, shifting a point directly illustrates the concept of transformation in geometry.