The correct answer is b: 13.
To find the shortest distance between locations B and C, we can use the Pythagorean theorem. The locations A, B, and C form a right triangle with A as the right angle. Here's how we can solve it step by step:
     1. Identify the Triangle:
            ○ Location A is the reference point.
            ○ Location B is north of A, so AB is the vertical side of the triangle.
            ○ Location C is east of A, so AC is the horizontal side of the triangle.
     2. Given Distances:
            ○ The distance AB = 5 km.
            ○ The distance AC = 12 km.
     3. Apply the Pythagorean Theorem:
            ○ The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
            ○ In this case, BC is the hypotenuse.
        $$BC^2 = AB^2 + AC^2$$
        $$BC^2 = 5^2 + 12^2$$
        $$BC^2 = 25 + 144$$
        $$BC^2 = 169$$
     4. Calculate BC:
            ○ To find BC, take the square root of 169.
        $$BC = \sqrt{169} = 13$$
     Therefore, the shortest distance between locations B and C is 13 km.