Based on this sketch of the assumed deflected position of the rigid bar, the initial length of rod $\left(1\right)$ is:

${\mathrm{L}}_{\mathrm{init}}={\mathrm{L}}_1$

and the length after deformation is:

${\mathrm{L}}_{\mathrm{final}}={\mathrm{L}}_1+{\mathrm{v}}_{\mathrm{A}}$

Therefore, the elongation of rod $\left(1\right)$ can be written as:

$$\begin{gathered} {\mathrm{\delta }}_1={\mathrm{L}}_{\mathrm{final}}-{\mathrm{L}}_{\mathrm{init}} \\ =({\mathrm{L}}_1+{\mathrm{v}}_{\mathrm{A}})-{\mathrm{L}}_1 \\ ={{\mathrm{v}}_{\mathrm{A}}}_{ \\ } \end{gathered}$$