Question

which transformations could have occurred to map △abc to △abc? a rotation and a dilation a rotation and a reflection a reflection and a dilation a translation and a dilation

Explanation:

Step1: Analyze the size change

The triangles have different sizes. A dilation changes the size of a figure.

Step2: Analyze the orientation change

The orientation of the triangles is different. A rotation changes the orientation of a figure.
Since there is a size - change (dilation) and an orientation - change (rotation), the transformations that could have occurred to map $\triangle ABC$ to $\triangle A''B''C''$ are a rotation and a dilation. A reflection would flip the figure over a line (which doesn't seem to be the case here as there is no mirror - like flipping that can be observed from the general shape and vertex order in a simple visual sense). A translation would just slide the figure without changing size or orientation (but the size is changed here).

Answer:

a rotation and a dilation