geometry

AP = AC = 9

Total walking distance = 20

Five friends live on the same street.

Their houses are at points A, B, C, D, and E, with the distances shown.

The five friends decide to meet at point P so that the total walking distance

for all five friends is minimized.
What is AP?

$\begin{array}{|ccccc|c|c|r|} \hline A & B&C&D&E &\text{Meet at} & \text{walking distance} &AP \\ & & & & & & \text{for all} \\ & & & & & & \text{five friends} \\ \hline 0&5&9&11&14&A&39&0\\ \hline 5&0&4&6&9&B&24&5 \\ \hline 9&4&0&2&5&C&\color{red}20&9 \\ \hline 11&6&2&0&3&D&22&11 \\ \hline 14&9&5&3&0&E&31&14 \\ \hline \end{array}$

The total walking distance
for all five friends is minimized at Point C and AP = 9