回復 1# P78961118 的帖子
\(\begin{align}
& \overline{PA}+\overline{PQ}+\overline{QB} \\
& =\sqrt{{{\left( a-10 \right)}^{2}}+{{5}^{2}}}+\sqrt{{{a}^{2}}+{{b}^{2}}}+\sqrt{{{5}^{2}}+{{\left( b-15 \right)}^{2}}} \\
\end{align}\)
看成\(x\)軸上一點\(C\left( a,0 \right)\),\(y\)軸上一點\(D\left( 0,b \right)\),\(E\left( 10,5 \right),F\left( 5,15 \right)\)
求\(\overline{CE}+\overline{CD}+\overline{DF}\)的最小值
作\(E\left( 10,5 \right)\)關於\(x\)軸的對稱點\(E'\left( 10,-5 \right)\);作\(F\left( 5,15 \right)\)關於\(y\)軸的對稱點\(F'\left( -5,15 \right)\)
則\(\overline{E'F'}\)的長即為所求