Question

identifying a sequence of similarity transformations
triangle def is similar to triangle def.
which similarity transformation could map △def to △def?
dilation and reflection
dilation and translation
rotation and dilation
rotation and reflection

Explanation:

Step1: Analyze dilation

Dilation is a transformation that changes the size of a figure but not its shape. Since \(\triangle DEF\) and \(\triangle D'E'F'\) are similar (same - shape but different - size), dilation must be part of the transformation.

Step2: Analyze rotation

Rotation is a transformation that turns a figure around a fixed point. By observing the orientation of the angles (for example, the angle at \(F\) in \(\triangle DEF\) and the angle at \(F'\) in \(\triangle D'E'F'\)), we can see that the orientation of the triangle has changed. A reflection would flip the figure over a line (changing the "handedness" in a more drastic way for non - symmetric figures in a plane), while a rotation can change the orientation of the figure in the plane without flipping it in the sense of a reflection. A translation would just slide the figure without changing orientation or size (but since the size is changed, translation is not the main orientation - changing transformation here).

Answer:

C. rotation and dilation