Answer:
[tex]\textsf{B.} \quad (x, y) \rightarrow (x - 4, y - 7)[/tex]
Step-by-step explanation:
A translation is a type of transformation and moves a figure left, right, up or down without changing its shape, size or orientation.
To determine the rule that translates triangle DEF to triangle D'E'F', we need to compare the coordinates of a pair of corresponding points and then identify the horizontal and vertical translations.
The coordinates of point D in triangle DEF are D(-1, 5).
The coordinates of point D' in triangle D'E'F' are D'(-5, -2).
To determine the translation rule, we can subtract the coordinate of the pre-image from the coordinate of the corresponding image point:
[tex]\textsf{Horizontal translation}=x_{D'}-x_{D}=-5-(-1)=-4[/tex]
[tex]\textsf{Vertical translation}=y_{D'}-y_{D}=-2-5=-7[/tex]
Therefore, the rule of translation that maps ΔDEF to ΔD'E'F' is to subtract 4 units from the x-coordinate and subtract 7 units from the y-coordinate:
[tex]\Large\boxed{\boxed{(x, y) \rightarrow (x - 4, y - 7)}}[/tex]
