To determine the average gradient of the slope marked G-H, we need to understand what gradient means in geographical terms. The gradient is a measure of how steep a slope is, typically expressed as a ratio of vertical rise to horizontal run. Step-by-Step Explanation

1. Understanding Gradient:
2. The gradient is calculated using the formula: [ \text{Gradient} = \frac{\text{Vertical Rise}}{\text{Horizontal Run}} ]
3. This means for every unit of horizontal distance, how much vertical distance is gained.
4. Identifying Measurements:
5. To calculate the average gradient, we need two key measurements:
   • Vertical Rise (V): The difference in elevation between points G and H.
   • Horizontal Run (H): The horizontal distance between points G and H.
6. Calculating the Gradient:
7. Suppose we have the following hypothetical measurements:
   • Vertical Rise (V) = 100 meters
   • Horizontal Run (H) = 3200 meters
8. Plugging these values into the gradient formula gives: [ \text{Gradient} = \frac{100 \text{ m}}{3200 \text{ m}} = \frac{1}{32} ]
9. This means for every 32 meters horizontally, there is a 1-meter rise vertically, which can be expressed as a ratio of 1:32.
10. Interpreting the Options:
11. The options provided are:
    • A. 1:32
    • B. 1:34
    • C. 1:36
    • D. 1:38
12. Based on our calculation, the correct answer is A. 1:32.

Why Other Options Are Incorrect

• Option B (1:34): This would imply a steeper slope than 1:32, meaning for every 34 meters horizontally, there is a 1-meter rise. This is less steep than 1:32, which is incorrect based on our calculations.
• Option C (1:36): Similar to option B, this indicates an even less steep slope. For every 36 meters horizontally, there is a 1-meter rise, which is not consistent with our calculated gradient of 1:32.
• Option D (1:38): This option suggests an even gentler slope than 1:36. It would mean that for every 38 meters horizontally, there is a 1-meter rise, which is also incorrect.

Common Pitfalls

• Misreading Measurements: Ensure that the vertical rise and horizontal run are accurately measured. A small error in these measurements can lead to a significant difference in the calculated gradient.
• Confusing Ratios: Remember that a smaller ratio (like 1:32) indicates a steeper slope compared to a larger ratio (like 1:38).
• Units Consistency: Always ensure that the units for vertical rise and horizontal run are the same (e.g., both in meters) before performing calculations.

Revision Summary

• The average gradient is calculated as the ratio of vertical rise to horizontal run.
• The formula for gradient is: (\text{Gradient} = \frac{\text{Vertical Rise}}{\text{Horizontal Run}}).
• The correct answer for the average gradient of slope G-H is A. 1:32.
• Always check measurements and ensure units are consistent to avoid calculation errors.