Understanding Point Positioning

This problem requires us to determine the relative direction of one point (U) with respect to another point (P) based on a series of directional movements. We can solve this by visualizing the positions on a 2D plane, similar to a coordinate system, or by calculating the coordinates of each point.

Step-by-Step Point Plotting

Let's use a coordinate system where East corresponds to the positive x-axis, West to the negative x-axis, North to the positive y-axis, and South to the negative y-axis. We'll start by setting a reference point.

1. Setting the Origin

Let's place point R at the origin (0, 0).

2. Positioning Point Q

Point Q is 4m towards the East of point R.

• R is at (0, 0).
• Moving 4m East means adding 4 to the x-coordinate.
• Coordinates of Q: (0 + 4, 0) = (4, 0).

3. Positioning Point P

Point P is 3m towards the South of point Q.

• Q is at (4, 0).
• Moving 3m South means subtracting 3 from the y-coordinate.
• Coordinates of P: (4, 0 - 3) = (4, -3).

4. Positioning Point S

Point S is 6m towards the South of point R.

• R is at (0, 0).
• Moving 6m South means subtracting 6 from the y-coordinate.
• Coordinates of S: (0, 0 - 6) = (0, -6).

5. Positioning Point T

Point T is 8m towards the West of point S.

• S is at (0, -6).
• Moving 8m West means subtracting 8 from the x-coordinate.
• Coordinates of T: (0 - 8, -6) = (-8, -6).

6. Positioning Point U

Point U is 3m North of point T.

• T is at (-8, -6).
• Moving 3m North means adding 3 to the y-coordinate.
• Coordinates of U: (-8, -6 + 3) = (-8, -3).

Note: The information about point V is not needed to find the direction of U with respect to P.

Calculating Direction: U with respect to P

Now we need to find the direction of point U from point P.

• Coordinates of P: (4, -3)
• Coordinates of U: (-8, -3)

To find the direction of U relative to P, we calculate the difference in their coordinates:

• Difference in x-coordinates (East-West): $ \Delta x = U_x - P_x = -8 - 4 = -12 $.
• Difference in y-coordinates (North-South): $ \Delta y = U_y - P_y = -3 - (-3) = -3 + 3 = 0 $.

Interpretation:

• $ \Delta x = -12 $: This means U is 12 units West of P.
• $ \Delta y = 0 $: This means U is neither North nor South of P; it lies on the same horizontal line (latitude) as P.

Since U is directly West of P (horizontal displacement only), the direction of U with respect to P is West.

Final Answer Determination

Based on our calculations, point U is located directly to the West of point P. Comparing this with the given options:

• 1. South-East
• 2. East
• 3. West
• 4. North-West
• 5. None of these

The calculated direction matches option 3.