A road network has parallel roads which are equidistant from each othe...
The road network consists of parallel roads that are equidistant from each other and run either north-south or east-west. The road junctions in this network are labeled as ABC, H, and X. We are given the following information about the positions of these junctions:
1. A is east of B and west of C.
2. H is southwest of C and southeast of B.
3. B is southeast of X.
Our task is to determine which junction is the farthest south and farthest east based on this information.
Finding the Farthest South Junction:
To find the farthest south junction, we need to identify the junction that is located at the lowest latitude. Let's analyze the given information to determine the southernmost junction:
- We know that H is southwest of C, which means H is located to the left and below C.
- A is east of B and west of C. Since we are looking for the southernmost junction, we can ignore the east-west relationship between A and B. This means that A can be located either south or north of B and C.
- B is southeast of X, which suggests that B is located to the right and below X.
Based on this information, we can conclude that the junction H is the farthest south because it is located to the left and below C. Therefore, the farthest south junction is H.
Finding the Farthest East Junction:
To find the farthest east junction, we need to identify the junction that is located at the highest longitude. Let's analyze the given information to determine the easternmost junction:
- We know that A is east of B and west of C. This means that A is located to the right of both B and C.
- H is southeast of B, which means H is located to the right and below B.
- B is southeast of X, suggesting that B is located to the right and below X.
Based on this information, we can conclude that the junction X is the farthest east because it is located to the right of both B and H. Therefore, the farthest east junction is X.
Summary:
Based on the given information, the farthest south junction is H, and the farthest east junction is X.