Question

The tourist bus center is located at (15,1) on a grid, and the bus station is located at (-1,-7). What are the coordinates (x, y) of the train station?

A) (-15, 7)
B) (-14, 6)
C) (16, 8)
D) (14, 8)

Answer 1

The coordinates of the train station, obtained by summing the x and y coordinates of the tourist bus center and bus station, are (14, -6). Thus, correct answer is option B.

Step-by-step explanation:

To ascertain the coordinates of the train station, it is essential to sum the x-coordinates and y-coordinates of both the tourist bus center and the bus station. Mathematically, this relationship is expressed as (xtrain, ytrain) = (xbus + xtourist, ybus + ytourist). By substituting the provided values, the equation becomes (xtrain, ytrain) = (-1 + 15, -7 + 1) = (14, -6).

Breaking it down further, the x-coordinate is determined by adding the x-coordinates of the bus station and the tourist bus center, yielding 14. Simultaneously, the y-coordinate is established by summing the y-coordinates of these locations, resulting in -6. Therefore, the coordinates of the train station manifest as (x, y) = (14, -6).

This numerical representation denotes the precise location of the train station on the coordinate plane. Such mathematical formulations prove invaluable in navigation and logistics, allowing for the accurate determination of spatial relationships between different points. In this scenario, the coordinates (14, -6) serve as the geometric descriptor for the train station's position in relation to the tourist bus center and the bus station.