Study the following information and answer the question. Point A is 8 metres to the west of point B. Point C is 4 metres to the south of point B. Point D is 4 metres to the east of point C. Point F is 6 metres to the north of point D. Point E is 8 metres to the west of point F. Point G is 2 metres to the south of point E. How far and in which direction is point G from point A?

Introduction / Context:
This question features several points placed relative to each other in a plane, described using directions and distances. The challenge is to compute the coordinates of each point step by step, and then determine the displacement from point A to point G. It is a typical reasoning problem that blends spatial visualisation with basic coordinate geometry and is often used to test careful reading and systematic tracking of multiple relationships.

Given Data / Assumptions:

• Point A is 8 metres west of point B.
• Point C is 4 metres south of point B.
• Point D is 4 metres east of point C.
• Point F is 6 metres north of point D.
• Point E is 8 metres west of point F.
• Point G is 2 metres south of point E.
• All directions are exact, and movements are along cardinal directions.
• We need the distance and direction from point A to point G.

Concept / Approach:
We will choose point B as the origin of a coordinate system for convenience. Then we can represent each point with coordinates based on its relative position to B or another known point. East is positive x, west negative x, north positive y and south negative y. After we compute coordinates for A through G, we find the displacement vector from A to G by subtracting coordinates. The magnitude and sign of this vector reveal the required distance and direction.

Step-by-Step Solution:
Step 1: Let point B be at (0, 0). Step 2: Point A is 8 metres to the west of B, so A is at (-8, 0). Step 3: Point C is 4 metres south of B, so C is at (0, -4). Step 4: Point D is 4 metres east of C. From (0, -4), moving 4 metres east gives D at (4, -4). Step 5: Point F is 6 metres north of D, so from (4, -4) we add 6 in the y direction to get F at (4, 2). Step 6: Point E is 8 metres west of F. From (4, 2), moving 8 metres west gives E at (-4, 2). Step 7: Point G is 2 metres south of E. From (-4, 2), moving 2 metres south gives G at (-4, 0). Step 8: Now we have A at (-8, 0) and G at (-4, 0). The displacement from A to G is found by subtracting coordinates: (-4, 0) minus (-8, 0) equals (4, 0). Step 9: A displacement of (4, 0) means G is 4 metres to the east of A.

Verification / Alternative check:
We can also reason qualitatively. Notice that A and B lie on a horizontal line with A 8 metres west of B. The construction from B down to C, across to D, up to F, and then west to E and south to G eventually brings G back to the same vertical level as A and B because G has y coordinate 0. Observing that E is 8 metres west of F, and F is 4 metres east of C, we find E is 4 metres west of C. Then G is 2 metres south of E, but this only changes the vertical coordinate, not the relative position to A along the horizontal axis at the y equals 0 line. Hence G must lie 4 metres east of A, confirming our calculation.

Why Other Options Are Wrong:

• Option B, 8 metres to the West, reverses both magnitude and direction; G is not further west than A.
• Option C, 4 metres to the West, has the correct magnitude but wrong direction.
• Option D, 8 metres to the East, doubles the correct magnitude.
• Option E, 2 metres to the South, describes a vertical displacement from E instead of from A and so is not relevant to the question asked.

Common Pitfalls:
With many points, it is easy to lose track of the intermediate coordinates or mix up east and west. Students may also forget that we are asked about G relative to A, not relative to B. Writing down coordinates step by step or drawing a simple grid significantly reduces the cognitive load and prevents errors in such multi stage reasoning problems.

Final Answer:
Point G is located 4 metres to the East of point A.