Topographic surveying concept: In relation to contour lines drawn on a map, the direction of the steepest slope (i.e., the line of maximum gradient) at any point is oriented how?

Introduction / Context:
Contours are lines joining points of equal elevation on a plan. Understanding how slope directions relate to contours is essential for designing roads, drains, retaining walls, and for interpreting topographic maps in civil engineering and land surveying. The question asks for the orientation of the steepest slope relative to the local contour line at a given point.

Given Data / Assumptions:

• Contours represent constant elevation; moving along a contour does not change elevation.
• Gradient is the rate of change of elevation per unit horizontal distance.
• We consider a smooth terrain surface where contours are well-behaved locally.

Concept / Approach:
A direction of maximum slope corresponds to the direction of the greatest rate of change of elevation. Since contours are level curves, the direction of the gradient of elevation is perpendicular to these level curves. Thus, the line of steepest descent (or ascent) is normal (at right angles) to the contour at the point considered.

Step-by-Step Solution:

Verification / Alternative check:
On a plan, closely spaced contours indicate steeper ground. The shortest line crossing the maximum number of contours per unit plan distance is the line drawn perpendicular to the contours—confirming the maximum gradient direction.

Why Other Options Are Wrong:

• Along the contour: elevation does not change; slope is zero.
• At 45°: an arbitrary angle; not guaranteed to be maximum slope.
• None of these: incorrect because a specific relationship exists (perpendicular).

Common Pitfalls:
Assuming the steepest line “follows” the contour spacing visually; confusing drainage flow direction with arbitrary downslope directions not checked against the perpendicular rule.

Final Answer:
At right angles (perpendicular) to the contour