A courier starts at the depot P(-2, 3), drives straight to Q(4, 11), then straight on to R(9, -1); the grid is marked in kilometres.
What total distance does the courier drive?

$PQ=\sqrt{(4+2{)}^2+(11-3{)}^2}=\sqrt{36+64}=10$ km and $QR=\sqrt{(9-4{)}^2+(-1-11{)}^2}=\sqrt{25+144}=13$ km. The two legs are driven one after the other, so the total is 10 + 13 = 23 km. $\sqrt{137}\approx 11.7$ km is the direct distance $PR$, a route the courier never takes; it is much shorter than 23 km, which is exactly why the delivery stop costs distance.