Final answer:
The dilation of triangle Δa'b'c' with a scale factor of 1/2 means that the triangle's dimensions are reduced to half their original size, supporting option 1 that Triangle Δa'b'c' is dilated by 1/2.
Step-by-step explanation:
The question is about finding the result of the dilation of triangle Δa'b'c' with a scale factor of 1/2. When we talk about dilation in the context of geometry, it means that we are resizing a figure without changing its shape. The scale factor determines how much the figure is enlarged or reduced. In this case, a scale factor of 1/2 means that each dimension of the triangle will be half of its original size. Therefore, all sides of the triangle will become half as long as they were, and the entire triangle will shrink in size accordingly.
There are several options listed in the question, but the correct choice is that Triangle Δa'b'c' is dilated by 1/2. This means option 1 is the correct answer. The other options suggest different scale factors that do not correspond to a dilation by 1/2.