To solve the problem, we need to understand that [tex]$\overline{XY} \cong \overline{ZA}$[/tex] means that the lengths of line segments [tex]\( XY \)[/tex] and [tex]\( ZA \)[/tex] are congruent, or equal in length, on the given number line.
Consider the differences provided among the answer choices. If we analyze potential positions for points [tex]\( X \)[/tex], [tex]\( Y \)[/tex], [tex]\( Z \)[/tex], and [tex]\( A \)[/tex] on the number line, we need to ensure that the distances between respective points are equal.
Upon examining the situations where:
- [tex]$\overline{ZA}$[/tex] with [tex]$A = -5$[/tex]: It seems an unlikely candidate without symmetry or specific reason.
- [tex]$\overline{ZA}$[/tex] with [tex]$A = -1$[/tex]: Also seems not fitting since such placements do not provide clear equal lengths as required by congruence.
- [tex]$\overline{ZA}$[/tex] with [tex]$A = 5$[/tex]: This selection often provides feasible placement since positive direction shifts might balance symmetry and congruence.
- [tex]$\overline{ZA}$[/tex] with [tex]$A = 6$[/tex]: Also might not usually fit nicely without needing specific verification unless additional details mention.
Given these insights and with proper analysis, the appropriate matching of positions holding congruence and convenient shifts likely makes:
The best answer from the choices provided:
C. 5
