Example 2. On the sides $\mathrm{AB}$ and $\mathrm{AC}$ of $\triangle \mathrm{ABC}$, determine points $P$ and $Q$ such that $B Q+Q P+P C$ is minimized.
As shown in Figure 3, construct the symmetric point $\mathrm{B}^{\prime}$ of point $\mathrm{B}$ with respect to $\mathrm{AC}$, and the symmetric point $\mathrm{C}^{\prime}$ of point $\mathrm{C}$ with respect to $\mathrm{AB}$. Connect $\mathrm{B}^{\prime} \mathrm{C}^{\prime}$, which intersects $\mathrm{AB}$ and $\mathrm{AC}$ at points $P$ and $Q$, respectively. Then points $P$ and $Q$ are the required points. This is because $\mathrm{BQ}+\mathrm{QP}+\mathrm{PC} = \mathrm{B}^{\prime} \mathrm{Q}+\mathrm{QP}+\mathrm{PC}^{\prime}=\mathrm{B}^{\prime} \mathrm{C}^{\prime}$