Final answer:
Without specific details or a diagram, the sequence of transformations from triangle DEF to triangle D' E' F' could include dilation, rotation, and translation. Exact transformations require more information such as vertex coordinates or visual representation.
Step-by-step explanation:
To determine the sequence of transformations that maps triangle DEF onto triangle D' E' F', one needs to consider various geometric transformations such as translation, reflection, rotation, and dilation (scaling). Typically, you might use the coordinates of the points or general properties of the transformations to deduce the sequence. Without specific coordinates or a diagram, a generic approach can be followed. We can look for a change in size, indicating a dilation. If the orientation of the triangle changes, it suggests a reflection or rotation has occurred. And if the position of the triangle changes without altering its size or orientation, we have a translation.
Suppose the sequence involved a dilation by factor 'k' from a center point O, followed by a rotation of 'θ' degrees around point O, and finally a translation by a vector v. Mathematically, if the original coordinates are (x,y), after dilation they become (kx, ky); after rotation, they become (x', y'); and after translation, the final coordinates are (x'+vx, y'+vy).
This explanation assumes a basic understanding of geometry and transformational sequence, but without a visual representation or additional information like coordinates, a precise sequence cannot be accurately described. Yet, this approach provides a guideline on how to proceed with such problems.