Question bank: Lines, Line Segments, and Rays

The following drawing represents a:

During a Geography class, the 6th-grade students were challenged to create a map of the city where they live, representing tourist attractions and main historical sites. To organize the information accurately, a group decided to use the notions of lines, segments, and rays from Mathematics, considering the meeting point of three main streets, A, B, and C, which form different angles. Street A is known for its straight layout and strategic function as a neighborhood divider, street B intersects street A at a right angle, and street C, which is not parallel to any of the other two, connects the ends of A and B. Assuming that the line segment formed by the intersection of A and B is represented by the central point of the map (0,0) and that each street is identified by a single direction of travel, determine the exact position of the tourist attraction point XYZ in relation to the intersection of streets A and B if it is located in the second quadrant of the Cartesian plane, considering the directions provided by the alignment of the streets and the map scale.

Consider a board game where players move pieces along straight line segments drawn on the board. In the game, there are two pieces A and B allocated at different points on the board. To achieve victory, a player must move their piece along the straight line segment that connects the points where pieces A and B are located. Pieces A and B are in places that form a straight line with a third point C, which is also on the board. Players must answer the following questions to advance in the game: 1) If a player can move their piece along a straight line segment connecting pieces A and B, what can we say about the relative position of the line segments formed by points A, B, and C? 2) If the line segments formed by points A, B, and C are concurrent, how can we classify the relative position of the lines passing through A and C and through B and C? Justify your answers based on the concepts of lines, segments, and rays.

In a coastal city, a team of urban planners is planning the construction of a new boardwalk that will connect two important tourist spots: the Freedom Lighthouse and the Sculpture Park. The project restricts the boardwalk to be built in a straight line and without interruptions between the two points. Furthermore, to ensure the safety of pedestrians, there is a need to signal pedestrian crossings parallel to the axis of the boardwalk, allowing to cross avenues at right angles. In a certain stretch of the boardwalk, it is identified the need to position a pedestrian crossing that starts exactly 20 meters from a corner and ends at a building that is aligned with the street that is desired to be crossed. Considering that the distribution of pedestrian crossings must follow safety standards without creating ambiguities in traffic and that all buildings and streets in the city are perfectly aligned, what is the nature of the segment where the pedestrian crossing should be painted and what is the position of the crossing with respect to the street and the boardwalk intersection?