Represent the following graphically a displacement of :
(i) 40 km, `30^(@)` west of south
(ii) 40 km, `30^(@)` east of south
(iii) 40 km, `30^(@)` west of north.

Answer

To represent the given displacements graphically, we will follow these steps for each of the three cases:

### Step-by-Step Solution:

1. **Draw the Coordinate Axes:**
- Start by drawing a vertical line to represent North-South.
- Draw a horizontal line intersecting it at the bottom to represent East-West.
- Label the top of the vertical line as North (N), the bottom as South (S), the right end of the horizontal line as East (E), and the left end as West (W).

2. **(i) 40 km, 30° West of South:**
- From the South point, measure an angle of 30° towards the West.
- Use a protractor to accurately measure this angle.
- From the South point, draw a line 40 km long in the direction of this angle.
- Label the endpoint of this line as Point A.

3. **(ii) 40 km, 30° East of South:**
- From the South point again, measure an angle of 30° towards the East.
- Draw a line 40 km long in this direction.
- Label the endpoint of this line as Point B.

4. **(iii) 40 km, 30° West of North:**
- From the North point, measure an angle of 30° towards the West.
- Draw a line 40 km long in this direction.
- Label the endpoint of this line as Point C.

5. **Final Representation:**
- You should now have three lines representing the three displacements:
- Line SA for 40 km, 30° West of South.
- Line SB for 40 km, 30° East of South.
- Line SC for 40 km, 30° West of North.
- Make sure to label each line clearly with its corresponding displacement.