Final answer:
Without specific details about quadrilateral ABCD, it is impossible to ascertain which line of reflection would map it onto itself. However, if assuming symmetry about the horizontal line y = 3, option d) 3y = 9 would be the correct choice for a line of reflection that maps ABCD onto itself.
Step-by-step explanation:
The question asks for the line of reflection that would map a geometric figure, such as quadrilateral ABCD, onto itself. A line of reflection that maps a figure onto itself would need to be either a line of symmetry of the figure or pass through the midpoint of every segment joining points and their images. Among the choices given, the correct line of reflection can be identified by understanding the properties of linear equations and reflection in geometry.
Examining the options:
a) y = ² /³x, b) y = 1 /³x, c) y = − 1 − ³x, d) 3y = 9 (which simplifies to y = 3), only option d) represents a horizontal line (y = 3) that could act as a line of reflection for a figure symmetric about the y = 3 line. Without additional information about the location of quadrilateral ABCD it is impossible to determine definitively which line would reflect it onto itself; however, assuming quadrilateral ABCD is symmetric about the y = 3 line, then d) is the candidate.