Final answer:
Avenue A is perpendicular to North Street, and it would also be perpendicular to South Street since they run parallel. The concept of vector components Ax and Ay, being perpendicular and analogous to these streets, helps illustrate the perpendicular relationship between Avenue A and South Street.
Step-by-step explanation:
Given that Avenue A is perpendicular to North Street, we can infer that Avenue A is also perpendicular to South Street because in a typical city grid, north and south streets run parallel to each other. When two lines are perpendicular to a third line, they are parallel to each other and form a 90° angle with the perpendicular line.
The relationships among vectors can help further illustrate this idea. If we look at the components of a vector, Ax and Ay, where Ax is the movement in the east-west direction (like Avenue A) and Ay is the movement in the north-south direction (like North Street), they form a right angle with each other. If you walk along Avenue A (the Ax component), then along North Street (the Ay component), you construct a path that is the resultant vector A with its own magnitude and direction.
The sum of these vectors is represented as Ax + Ay = A. This combination holds only for vector quantities, which include both magnitude and direction. This principle does not apply when we're summing up the magnitudes alone, as in the example where if Ax is 3 m east and Ay is 4 m north, the direct path A would not simply be their sum in magnitudes but would instead be a diagonal 5 m northeast according to the Pythagorean theorem.