Final answer:
To determine the transformation notation that maps triangle ABC onto DEF, one must analyze the positions and properties of both triangles to ascertain if the transformation is a translation, reflection, rotation, or dilation. Transformation notations are used to describe these specific movements mathematically.
Step-by-step explanation:
To determine which transformation notation maps triangle ABC onto triangle DEF, one would typically observe the characteristics of the two triangles in their respective positions. The transformation could be a translation, reflection, rotation, or dilation. Translations involve sliding the figure in a given direction, reflections involve flipping the figure over a line, rotations turn the figure about a point, and dilations resize the figure proportionally.
When matching transformation notations to graphs, it is important to look for changes in size, which suggest dilation, orientation changes, which may indicate a rotation or reflection, and shifts in position, which suggest a translation. Specific notation for these transformations might look like T(x, y) for translation by x units horizontally and y units vertically, R(θ) for rotation by an angle θ, ref(line) for reflection across a line, and D(k) for dilation by a scale factor k.