Question

A person walks 3 km north, then turns east and walks 4 km, then turns south and walks 3 km. How far is he from his starting point?

• A. 7 km
• B. 4 km
• C. 5 km
• D. 3 km

Hint:

• Use a coordinate system (e.g., starting at origin (0,0)). North is +y, East is +x, South is -y, West is -x.
• Track the coordinates after each movement.
• Calculate the distance between the starting point and the final point using the distance formula $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$.
• Or, visualize the path: North and South movements can cancel out. East and West movements can cancel out.

Answer 1

The Correct Option is B

Let the starting point be $O$ (origin at coordinates $(0, 0)$).

• Walks 3 km north: Reaches point $A$ at $(0, 3)$.
• Turns east and walks 4 km: Reaches point $B$ at $(4, 3)$.
• Turns south and walks 3 km: Reaches point $C$ at $(4, 0)$.

The starting point is $O(0, 0)$ and the final point is $C(4, 0)$.
Distance from starting point to final point: \[ OC = \sqrt{(4 - 0)^2 + (0 - 0)^2} = \sqrt{16} = 4 \text{ km} \] Alternatively, visualize the path:

• 3 km north, then 3 km south — net vertical displacement = 0
• 4 km east — net horizontal displacement = 4 km

Therefore, the net displacement is 4 km east of the starting point. \[ \boxed{4 \text{ km}} \]