Question

The grid below shows the location of 3 places in a neighborhood.



If the hotel is 3 units directly east of the gym, which of the following ordered pairs best represents the hotel's location?

A.
(5, 3)
B.
(5, 9)
C.
(8, 6)
D.
(6, 2)

Answer 1

To determine the location of the hotel based on the information provided, we need to identify the location of the gym first.

Let's say the gym's location is at point \( (x, y) \). Since the hotel is 3 units directly east of the gym, the hotel's coordinates would be \( (x + 3, y) \).

Now, let's examine each of the provided options to see if they can represent the hotel location depending on the gym's position.

1. **A. (5, 3)**
This means the hotel is at \( (5, 3) \), hence the gym must be at \( (5 - 3, 3) = (2, 3) \). This is a possible location.

2. **B. (5, 9)**
This means the hotel is at \( (5, 9) \), hence the gym must be at \( (5 - 3, 9) = (2, 9) \). This is also a possible location.

3. **C. (8, 6)**
This means the hotel is at \( (8, 6) \), hence the gym must be at \( (8 - 3, 6) = (5, 6) \). This is another possible option.

4. **D. (6, 2)**
This means the hotel is at \( (6, 2) \), hence the gym must be at \( (6 - 3, 2) = (3, 2) \). This is another possible location.

As there is no specific initial position given for the gym, we cannot definitively determine the location of the hotel without knowing the gym's coordinates. However, since all options convert back consistently to a valid gym location by moving 3 units west, any of these options could theoretically represent the hotel.

If you have the specific coordinates of the gym, or if there are more clues available, that would help narrow it down further. But based solely on the information given, one possible answer for the ordered pair representing the hotel's location is:

**C. (8, 6)**