An ant crawls straight from $(-4,6)$ to the origin, and then continues straight on to $(4,3)$. How far does it travel?

Answer 1

first leg
4^2 + 6^2 = 16 + 36 = 54
sqrt 52 = 7.21
second leg
3,4,5 triangle so 5
7.21 + 5 = 12.2
That is how far it TRAVELLED (sum on the ant odometer)
However the straight line displacement from (-4,6) to (4,3) is
sqrt (8^2 + 3^2) = sqrt(64+9) = sqrt (73) = 8.54