A person travels 4 km towards north and then travels 5 km Eastwards. He then travels 10 km rightwards, and then 3 km to the left and finally 5 km northwards how far is he approximately from his original starting point and in what direction?

Let's break down the movements step by step: 1. The person starts at the origin point (0, 0). 2. Travels 4 km north: This takes him to (0, 4). 3. Travels 5 km east: This takes him to (5, 4). 4. Travels 10 km rightwards: From (5, 4), moving right (east) takes him to (15, 4). 5. Travels 3 km to the left: From (15, 4), moving left (west) takes him to (12, 4). 6. Finally, travels 5 km north: From (12, 4), moving north takes him to (12, 9). Now we find the distance from the original starting point (0, 0) to the final position (12, 9). Using the distance formula: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substituting in our values: \[ \text{Distance} = \sqrt{(12 - 0)^2 + (9 - 0)^2} = \sqrt{12^2 + 9^2} = \sqrt{144 + 81} = \sqrt{225} = 15 \text{ km} \] **Final Result:** The person is approximately 15 km from the starting point in the direction of northeast.