Shortest Distance Questions

A man walks $3\text{km}$ North, then turns East and walks $4\text{km}$, then turns South and walks $3\text{km}$, then turns West and walks $2\text{km}$. What is his shortest distance now from the starting point and in which direction is he from his starting point?

Arjun starts from his home in a car and drives $500\text{m}$ towards the South. He then takes a left turn and drives $500\text{m}$. After that, he drives $500\text{m}$ towards the North. Next, he takes a right turn and drives $100\text{m}$, then takes another right turn and drives $800\text{m}$. Finally, he takes one more right turn and drives $600\text{m}$ to reach his friend’s house. What is the shortest distance from his home now and in which direction is Arjun from his home?