Answer: The correct option is (D) double reflection.
Step-by-step explanation: We are given to select the correct composition that will map figure Z onto figure R and then onto figure J.
From the figure, we note that
the co-ordinates of the vertices of the figure Z are (0, 2), (1, 2), (4, 5) and (1, 4).
The co-ordinates of the vertices of the figure R are (0, 2), (-1, 2), (-4, 5) and (-1, 4).
The co-ordinates of the vertices of the figure J are (0, -2), (-1, -2), (-4, -5) and (-1, -4).
We know that, if a point is getting reflected over Y-axis, then its co-ordinates will change according to the rule (x, y) ⇒ (-x, y).
So, if the figure Z is reflected over Y-axis, then its co-ordinates will become
(0, 2) ⇒ (0, 2),
(1, 2) ⇒ (-1, 2),
(4, 5) ⇒ (-4, 5)
and
(1, 4) ⇒ (-1, 4).
These are the co-ordinates of the vertices of figure R, so first transformation is a reflection.
Again, if we reflect the figure R over X-axis, then the co-ordinates of the vertices will change according to the rule (x, y) ⇒ (x, -y).
So, the vertices of figure R will become
(0, 2) ⇒ (0, -2),
(-1, 2) ⇒ (-1, -2),
(-4, 5) ⇒ (-4, -5)
and
(-1, 4) ⇒ (-1, -4).
Thus, the required compositions that will map figure Z onto figure R and then onto figure J are reflection and reflection, .i.e., double reflection.
Option (D) is the correct option.