Convex Combination of $\underline{a}_1, \underline{a}_2$:
\[
   \underline{x}
   =
   \underline{a}_1+t\underline{a}_{12}
   =
   \underline{a}_2+t'\underline{a}_{21},
   \quad t=1-t' \in \mathbb{R}
\]
$\underline{a}_{12}=\underline{a}_{2}-\underline{a}_{1}$.

Particularly, for $\underline{p}_1$:

\[
   \underline{p}_1
   =
   \underline{a}_1+t_1 \underline{a}_{12}
   =
   \underline{a}_2+t_1' \underline{a}_{21}
\]

And $\underline{p}_2$:

\[
   \underline{p}_2
   =
   \underline{a}_1+t_2 \underline{a}_{12}
   =
   \underline{a}_2+t_2' \underline{a}_{21}
\]