Final answer:
The question seems to be incomplete as it lacks the scaling factor for the dilation transformation (D). Without this information, it is not possible to determine the image point of (0, -5) after the transformation D;oT(2, -1).
Step-by-step explanation:
The question is asking for the image point of the original point (0, -5) after a geometric transformation. The notation D;oT(2, −1) implies that the transformation is a dilation (D) centered at the origin (o) followed by a translation (T) by the vector (2, -1). However, the question does not provide clear specifics about the scaling factor for the dilation, which is necessary to carry out the dilation transformation.
If we were to assume that the scaling factor of the dilation (D) is 1 (meaning no dilation), the point (0, -5) would remain unchanged after the dilation. Then, the translation (T) by the vector (2, -1) would be applied, moving the point 2 units to the right and 1 unit up, resulting in finding the image point (2, -4). However, since none of the provided answers match this image point, and the scaling factor is unknown, the question cannot be answered definitively without additional information.