Final answer:
Dilation in geometry is a transformation centered at a point O, creating an image with the same shape but different size. To confirm dilation, points should move radially from point O, maintaining their relative orientations. A coordinate system can depict dilation by applying a scale factor to point coordinates.
Step-by-step explanation:
The question refers to dilation in geometry, which is a transformation that produces an image that is the same shape as the original, but is a different size. When a figure is dilated with respect to a center point O, every point of the figure moves along a straight line away from or towards O. The distance each point moves is proportional to its distance from O. The resulting image is either an enlargement or reduction of the original figure based on the scale factor used in the dilation.
To determine if a described diagram shows a dilation centered at point O, we would expect to see that points in the figure have moved radially away from or towards point O, in such a way that the angles between lines connecting corresponding points before and after the dilation are all congruent. In other words, new positions of dilated points should maintain their relative orientations to point O and to each other.
An example of dilation can be represented in a coordinate system by applying a scale factor to the coordinates of points of the figure. Assuming the center of dilation is the origin (0, 0), the coordinates of a point P after dilation with a scale factor k will be (k × Px, k × Py), where Px and Py are the original coordinates of P.