Answer: The length of A'B' is 4 units.
Step-by-step explanation: Given that the line segment AB has a length of 4 units and it is translated 2 units to the right on a coordinate plane to obtain line segment A'B'.
We are to find the length of A'B'.
According to the given information, the line segment AB is translated 2 units to the right.
So, the point A and B, both will be translated two units to the right.
Let us consider the co-ordinates of the endpoints of AB are (1, 2) and (5, 2), so that the length of AB (using distance formula) is
[tex]AB=\sqrt{(5-1)^2+(2-2)^2}=\sqrt{16}=4~\textup{units}.[/tex]
After translating 2 units right, the point A will translate to A'(3, 2) and B will translate to B'(7, 2).
Therefore, the length of A'B' will be
[tex]A'B'=\sqrt{(7-3)^2+(2-2)^2}=\sqrt{16}=4~\textup{units}.[/tex]
Thus, the length of A'B' is 4 units.
