Raju walks 4 km towards the East from his starting point and then turns left to walk another 3 km towards the North.\nIn which cardinal direction and at what straight-line distance is he now located from his initial position?

Introduction / Context:
Direction sense test questions check your ability to mentally track movements on an imaginary map and then identify the final position and direction of a person with respect to the starting point. In this problem, Raju first walks along the East direction and then turns left, which makes him face North. We are asked to determine both the resulting direction and the straight-line distance from his starting position, which is a classic right-angled triangle situation in basic geometry.

Given Data / Assumptions:

• Raju starts from an initial point taken as the origin.
• He walks 4 km towards the East.
• He then turns left and walks 3 km, which means he now walks towards the North.
• We use the standard convention: North is up, East is to the right, South is down and West is to the left on a map.
• We assume he walks in straight lines and the turns are exact right angles.

Concept / Approach:
The movement described forms a right-angled triangle when we join the starting point and the final point. The leg along the East direction is 4 km and the leg along the North direction is 3 km. The shortest distance from the starting point to the final point is the hypotenuse of this triangle. By using the Pythagoras theorem, distance^2 = (horizontal displacement)^2 + (vertical displacement)^2. The direction is determined by noticing that the final point lies to the East and North of the origin, which corresponds to the North-East direction.

Step-by-Step Solution:
Step 1: Mark the starting point as O at coordinates (0, 0). Step 2: Walking 4 km East takes Raju to point A with coordinates (4, 0). Step 3: From facing East, a left turn means facing North. Walking 3 km North from A takes him to point B with coordinates (4, 3). Step 4: Compute the straight-line distance OB using Pythagoras theorem: OB^2 = 4^2 + 3^2 = 16 + 9 = 25. Step 5: Therefore, OB = √25 = 5 km, so the distance from the starting point to the final point is 5 km. Step 6: Since the final coordinates (4, 3) are both positive, Raju is to the East and to the North of the starting point, which means he is in the North-East direction.

Verification / Alternative check:
A quick mental check is that the numbers 3, 4 and 5 form a well-known Pythagorean triplet. Whenever two perpendicular legs measure 3 and 4 units, the hypotenuse is 5 units. Here, one leg is 3 km and the other is 4 km, so 5 km is immediately reasonable. Also, because the path is “right then up” (East then North), the final position must lie in the North-East quadrant relative to the start. Both distance and direction are thus fully consistent with the detailed calculation.

Why Other Options Are Wrong:
South-West, 5 km is incorrect because Raju never travels towards the South or West overall; his net movement is towards the East and North. South-East, 5 km is wrong because there is no net movement towards the South; the final vertical movement is upwards. North-West, 5 km is also incorrect because there is no net displacement towards the West. North, 7 km is incorrect as the total displacement is not 7 km and also includes an Eastward component, so it cannot be purely North.

Common Pitfalls:
Students often confuse the direction after a left or right turn, especially when they do not explicitly imagine themselves facing the initial direction. Another common mistake is to simply add the distances 4 km and 3 km to get 7 km as the answer, forgetting that they are perpendicular displacements, not movements along the same straight line. Some learners also mislabel the quadrant and might claim South-East or North-West without plotting the final coordinates carefully. Drawing a small diagram with arrows for each move is a very reliable way to avoid these errors.

Final Answer:
Raju is finally at a point that is North-East, 5 km from his initial position.