In airport planning, two runways have end coordinates (5000, 5000)–(8000, 7000) and (4600, 5100)–(7000, 5300). Determine the Airport Reference Point (A.R.P.) by averaging the geometric midpoints of all runways.

Introduction:
In airport engineering, the Airport Reference Point (A.R.P.) is a designated geographical position that represents the approximate center of the aerodrome. For a system of runways, a common approach is to compute the A.R.P. as the average of the midpoints of the individual runways, giving a balanced reference for charts, surveys, and navigation data.

Given Data / Assumptions:

• Runway 1 endpoints: (5000, 5000) and (8000, 7000).
• Runway 2 endpoints: (4600, 5100) and (7000, 5300).
• A.R.P. taken as the mean of runway midpoints.

Concept / Approach:

The midpoint of a line with endpoints (x1, y1) and (x2, y2) is ((x1 + x2) / 2, (y1 + y2) / 2). The A.R.P. is then computed as the average of all runway midpoints when multiple runways exist.

Step-by-Step Solution:

Verification / Alternative check:

The two midpoints lie reasonably close; their average must fall between them. (6150, 5600) lies between (6500, 6000) and (5800, 5200), confirming plausibility.

Why Other Options Are Wrong:

• (6500, 6000): This is only the midpoint of Runway 1, not the average of both runways.
• (5800, 5200): This is only the midpoint of Runway 2.
• (8000, 7000): This is an endpoint, not a representative center.
• (6200, 5550): A nearby estimate but not the exact computed average.

Common Pitfalls:

• Choosing the midpoint of the longest runway instead of averaging all runways.
• Accidentally averaging endpoints directly rather than averaging midpoints.

Final Answer:

(6150, 5600)