Bill walks 1/2 mile south, then 3/4 mile east, and finally 1/2 mile south. how many miles is he, in a direct line, from his starting point? express your answer as a decimal to the nearest hundredth.

1.25 mi

Step-by-step explanation:

Think of this in terms of a graph in the x-y axis

Bill starts out at point (0,0)

He walks 1/2 mile south (i.e 0.5 miles in the -y direction) and ends up at (0,-0.5)

Next he walks 3/4 mile (0.75 miles) in the +x direction and ends up at (0.75, -0.5)

Then he continues to walk 1/2 mile (0.5 miles) in south in the -y direction and ends up at (0.75, -1).

His final distance from the starting point (0,0) from his end point (0.75,-1) is simply the distance between the 2 coordinates (see picture for formula).

hence,

D = √ (0.75 -0)² + (-1 - 0)²

D = √ (0.75)² + (-1)²

D = 1.25