To determine the approximate gradient between point X and the trigonometrical station, we need to understand what gradient means in a geographical context. The gradient is a measure of the steepness or incline of a slope, typically expressed as a ratio of vertical change (rise) to horizontal change (run). Step-by-Step Explanation

1. Understanding Gradient:
2. The gradient is calculated using the formula: [ \text{Gradient} = \frac{\text{Vertical Change (Rise)}}{\text{Horizontal Change (Run)}} ]
3. This means if you have a rise of 1 unit for every 7 units of horizontal distance, the gradient is 1:7.
4. Identifying the Points:
5. In this scenario, we have two points: point X and the trigonometrical station. To find the gradient, we need to know the elevation (height) of both points and the horizontal distance between them.
6. Calculating the Gradient:
7. Suppose the elevation of point X is lower than that of the trigonometrical station. If the elevation difference (rise) is, for example, 100 meters and the horizontal distance (run) is 1300 meters, we can calculate the gradient as follows: [ \text{Gradient} = \frac{100 \text{ m}}{1300 \text{ m}} = \frac{1}{13} ]
8. This means for every 13 meters of horizontal distance, there is a 1-meter rise, which corresponds to a gradient of 1:13.
9. Interpreting the Options:
10. The options provided are:
    • A. 1:7
    • B. 1:9
    • C. 1:11
    • D. 1:13
11. Since we calculated a gradient of 1:13, option D is the correct answer.

Why Other Options Are Incorrect

• Option A (1:7): This would imply a very steep slope where for every 7 meters of horizontal distance, there is a 1-meter rise. This is steeper than what we calculated.
• Option B (1:9): Similar to option A, this indicates a steeper slope than our calculated gradient. For every 9 meters horizontally, there would be a 1-meter rise, which does not match our findings.
• Option C (1:11): This option suggests a slope that is still steeper than our calculated gradient. For every 11 meters of horizontal distance, there would be a 1-meter rise, which again does not align with our calculation.

Common Pitfalls

• Misreading Elevation: Ensure that you accurately read the elevation of both points. A small error in elevation can lead to a significant difference in the calculated gradient.
• Horizontal Distance Measurement: Make sure to measure the horizontal distance correctly. Sometimes, the path taken may not be a straight line, which can affect the run measurement.
• Understanding Ratios: Be clear on what the ratio means. A smaller second number in the ratio indicates a steeper slope.

Revision Summary

• The gradient is calculated as the ratio of vertical change to horizontal change.
• The correct gradient between point X and the trigonometrical station is 1:13.
• Other options (1:7, 1:9, 1:11) represent steeper slopes than the calculated gradient.
• Always double-check elevation and distance measurements to avoid calculation errors.

By understanding these concepts and calculations, you can confidently approach similar questions in your geography exams.