This question requires us to determine the directional relationship between two points, E and A, based on a series of given spatial relationships between different points. We need to carefully map out the positions of the points to find the direction of E relative to A.

Mapping Point Positions

Let's break down the given information and establish the coordinates or relative positions of the points. We can set a reference point, for example, placing point C at the origin (0,0) for easier calculation.

• Statement 3: Point C is 9 km to the east of point A. This implies that point A is 9 km to the west of point C.
  • If C = (0, 0), then A = (-9, 0).
• Statement 4: Point E is 8 km to the north of point C.
  • If C = (0, 0), then E = (0, 8).

We have now determined the positions of A and E relative to C. Point A is 9 km West of C, and Point E is 8 km North of C.

Determining Direction of E from A

To find the direction of point E from point A, we look at the displacement needed to move from A to E.

• Current position (Point A): (-9, 0)
• Target position (Point E): (0, 8)

Calculate the change in coordinates:

• Change in East-West direction (x-axis): $0 - (-9) = +9$ km. A positive value indicates movement towards the East.
• Change in North-South direction (y-axis): $8 - 0 = +8$ km. A positive value indicates movement towards the North.

Since the movement from A to E involves displacement in both the East and North directions (9 km East and 8 km North), the direction of E from A is North-East.

Analysis of Other Statements

The other statements provided in the question help to establish the positions of points B, D, G, and H. However, they are not necessary for finding the direction of E from A. Let's verify them for completeness:

• Statement 1: Point B is 6 km to the west of point E. If E = (0, 8), then B = ($0 - 6$, 8) = (-6, 8).
• Statement 6: Point D is 10 km to the south of point B. If B = (-6, 8), then D = (-6, $8 - 10$) = (-6, -2).
• Statement 2: Point D is 2 km to the south of point H. If D = (-6, -2), then H = (-6, $-2 + 2$) = (-6, 0).
• Statement 5: Point G is 3 km to the west of point B. If B = (-6, 8), then G = ($-6 - 3$, 8) = (-9, 8).

These additional coordinates confirm the relative positioning but do not alter the calculation for the direction of E from A.

Conclusion

Based on the calculations, point E is located 9 km East and 8 km North of point A. Therefore, the direction of point E from point A is North-East.