Using translation concepts, it is found that:
- The rotation applied to triangle DEF to create triangle D′E′F′ is (x, y) → (−x, −y).
- The location of T'' is at (-2,-4).
What is a translation?
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For the two triangles, the vertices are given as follows:
- D(-1, 6) and D' (1, -6), that is, (x,y) -> (-x,-y).
- E(1,3) and E' (-1, -3), that is, (x,y) -> (-x,-y).
- F(6,3) and F'(-6, -3), that is, (x,y) -> (-x, -y).
Hence:
The rotation applied to triangle DEF to create triangle D′E′F′ is (x, y) → (−x, −y).
For the rectangle, vertex T is at (-2,6), hence, for the first translation:
T': (- 2 - 2, 6 - 4) -> (-4, 2).
The rule for a 90º counterclockwise rotation is given by:
(x,y) -> (-y,x).
Hence:
T'': (-4, 2) -> (-2,-4).
The location of T'' is at (-2,-4).
More can be learned about translation concepts at https://brainly.com/question/4521517
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