Solving Direction and Distance Problems

This question asks us to find the final position of worker K relative to the final position of worker L after they both follow specific paths involving directions and distances. To solve this, we can track the movements of each worker step-by-step.

Tracking Worker K's Journey

Let's assume the starting point for both workers is the origin (0,0) on a coordinate plane, where North is along the positive Y-axis, South is along the negative Y-axis, East is along the positive X-axis, and West is along the negative X-axis.

Worker K's movements:

• Starts at (0,0).
• Walks 5 km North: Moves 5 units in the positive Y direction. Current position: (0, 0 + 5) = (0, 5).
• Turns right (which is East from North) and walks 2 km: Moves 2 units in the positive X direction. Final position of K: (0 + 2, 5) = (2, 5).

So, worker K ends up at the coordinates (2, 5).

Following Worker L's Path

Worker L's movements from the same starting point (0,0):

• Starts at (0,0).
• Walks 3 km West: Moves 3 units in the negative X direction. Current position: (0 - 3, 0) = (-3, 0).
• Turns South and walks 4 km: Moves 4 units in the negative Y direction. Current position: (-3, 0 - 4) = (-3, -4).
• Finally, turns left (which is East from South) and walks 5 km: Moves 5 units in the positive X direction. Final position of L: (-3 + 5, -4) = (2, -4).

So, worker L ends up at the coordinates (2, -4).

Calculating Relative Position of K with Respect to L

We need to find where K is located when observed from L's final position. K is at (2, 5) and L is at (2, -4).

To find the position of K relative to L, we can subtract L's coordinates from K's coordinates:

\(\text{Relative Position} = \text{Position of K} - \text{Position of L}\)

\(\text{Relative Position} = (2, 5) - (2, -4)\)

\(\text{Relative Position} = (2 - 2, 5 - (-4))\)

\(\text{Relative Position} = (0, 5 + 4)\)

\(\text{Relative Position} = (0, 9)\)

The resulting vector (0, 9) means there is no difference in the X direction (East/West) and a difference of +9 in the Y direction (North/South). Since positive Y represents North, K is 9 km North of L.

Comparing with Options

Let's check our result against the given options:

• K is 1 km South of L (Incorrect)
• K is 9 km North of L (Correct)
• K is 9 km South of L (Incorrect)
• K is 1 km North of L (Incorrect)

Our calculation shows that K is 9 km North of L.

Revision Table: Key Movements

Additional Information: Directions and Turns

Understanding directions and turns is crucial in solving spatial reasoning problems.

• Cardinal Directions: North, South, East, West.
• Relative Turns: 'Right' and 'Left' turns depend on the current direction of movement.
  • From North, Right turn is East, Left turn is West.
  • From South, Right turn is West, Left turn is East.
  • From East, Right turn is South, Left turn is North.
  • From West, Right turn is North, Left turn is South.
• Using Coordinates: A simple way to track movements is using a 2D coordinate system.
  • North increases Y.
  • South decreases Y.
  • East increases X.
  • West decreases X.

By consistently applying these rules, you can accurately determine final positions and relative locations.