Finding the Shortest Distance Between Persons A and G

This problem requires us to determine the relative positions of all persons based on the given directional and distance information and then calculate the shortest distance between A and G. The shortest distance between two points in a 2D plane is a straight line, which can be calculated using the distance formula.

Analyzing the Given Positions

Let's list the given relationships:

• B is 11 meters north of C.
• A is 12 meters to the west of B.
• D is 20 meters south of E.
• C is 20 meters west of D.
• G is 3 meters north of F.
• F is 27 meters to the west of E.

Determining Coordinates (Relative Positioning)

We can set up a coordinate system to represent the positions. Let's assume C is at the origin (0,0) for simplicity.

• C: (0, 0)
• B is 11 meters north of C: B is at (0, 11).
• A is 12 meters west of B: A is at (0 - 12, 11) = (-12, 11).
• C is 20 meters west of D: D is 20 meters east of C. D is at (0 + 20, 0) = (20, 0).
• D is 20 meters south of E: E is 20 meters north of D. E is at (20, 0 + 20) = (20, 20).
• F is 27 meters west of E: F is at (20 - 27, 20) = (-7, 20).
• G is 3 meters north of F: G is at (-7, 20 + 3) = (-7, 23).

So, the coordinates of the relevant persons are:

• A: (-12, 11)
• G: (-7, 23)

Calculating the Shortest Distance

The shortest distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula:

\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Using the coordinates for A (-12, 11) and G (-7, 23):

Distance AG = $\sqrt{(-7 - (-12))^2 + (23 - 11)^2}$

Distance AG = $\sqrt{(-7 + 12)^2 + (12)^2}$

Distance AG = $\sqrt{(5)^2 + (12)^2}$

Distance AG = $\sqrt{25 + 144}$

Distance AG = $\sqrt{169}$

Distance AG = 13 meters.

Conclusion

The shortest distance between person A and person G is 13 meters.