Answer: The correct option is
(D) C'D' and CD are equal in length.
Step-by-step explanation: We are given that a line segment CD shown on a co-ordinate grid in the graph.
The line segment CD is reflected about the y-axis to form C'D'.
We are to select the statement that describes C'D'.
From the graph, we see that the co-ordinates of the endpoints of line segment CD are C(1, 2) and D(1, -1).
We know that
if a point (x, y) is reflected about the Y-axis, then its co-ordinates changes to (-x, y).
So, after reflection about Y-axis, the co-ordinates of the points C and D changes to
C(1, 2) ⇒ C'(-1, 2),
D(1, -1) ⇒ D'(-1, -1).
Now, the length of CD as calculated using distance formula is
[tex]L_{CD}=\sqrt{(-1-2)^2+(1-1)^2}=\sqrt9=3~\textup{units},\\\\L_{C'D'}=\sqrt{(-1-2)^2+(-1+1)^2}=\sqrt{9}=3~\textup{units}.[/tex]
Thus, the lengths of CD and C'D' are equal.
Option (D) is CORRECT.
