Answer:
The location of Balloon C relative to the tower is 3 miles west and 4 miles south (Option B).
Step-by-step explanation:
To find the location of Balloon C, we first determine the positions of Balloons A and B. Balloon A is 5 miles east and 8 miles south of the tower, while Balloon B is 7 miles west and 10 miles north. The distance between A and B is the hypotenuse of a right-angled triangle formed by their positions.
Now, Balloon C is located four-ninths of the distance from Balloon A to Balloon B. Calculating this distance ratio and applying it to the horizontal and vertical displacements between A and B, we find that Balloon C is 3 miles west and 4 miles south relative to the tower.
Understanding geometric relationships and ratios is crucial in solving location problems involving multiple points.
Option b is correct.