Question

Instead of turning right at the end if he took left and walked 20 km, what is the shortest distance to his starting point?

• A. \(3\sqrt{7}\) km
• B. \(2\sqrt{5}\) km
• C. \(7\sqrt{2}\) km
• D. \(5\sqrt{2}\) km

Hint:

Translate every turn into a direction on the \(xy\)-plane and keep running coordinates. Then use the Pythagorean theorem for the straight-line distance.

Answer 1

The Correct Option is D

Step 1: Net east-west displacement \(=-25+30=+5\) km; net north-south displacement \(=-15+20=+5\) km.

Step 2: Straight-line distance \(=\sqrt{5^2+5^2}=\sqrt{50}\).

Step 3: Simplify: \(\sqrt{50}=5\sqrt{2}\) km.
\[ \boxed{5\sqrt{2}\ \text{km}} \]