Answer:
Option D. a 180° rotation about the origin and then a translation left 8 units.
Step-by-step explanation:
See the attached figure_1
From the graph: Point A'(-12,-6) is the image of point A(4,6)
We will check which sequence of transformations is true:
A. a reflection across the y-axis and then a translation down 16 units
A(4,6) ⇒(-4,6)⇒(-4,-10) (Wrong sequence)
B. a 90° counterclockwise rotation about the origin and then a translation down 8 units
A(4,6) ⇒(-6,4)⇒(-6,-4) (Wrong sequence)
C. a 90° clockwise rotation about the origin and then a translation left 16 units
A(4,6) ⇒(6,-4)⇒(-10,-4) (Wrong sequence)
D. a 180° rotation about the origin and then a translation left 8 units
A(4,6) ⇒(-4,-6)⇒(-12,-6)A' (True sequence)
Note: the rules is the attached figure_2
