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Question about Lines, Line Segments, and Rays

Subject Mathematics

Mathematics

Source Originais Teachy

Originais Teachy

Topic Lines, Line Segments, and Rays

Lines, Line Segments, and Rays

Difficulty Medium

Medium

(Originais Teachy 2024) - Question Medium of Mathematics

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?

The nature of the segment where the pedestrian crossing should be painted is a line. The position of the crossing with respect to the street and boardwalk intersection is parallel to the street, 20 meters away from the corner.

The position of the crossing with respect to the street and boardwalk intersection should be diagonal to the corner, connecting two equidistant points from it.

The orientation of the pedestrian crossing should be perpendicular to the direction of the boardwalk, starting at the building and ending exactly at the corner, 20 meters from the start.

The pedestrian crossing should be painted on a line segment that connects the opposite corner to the destination building, forming a 45-degree angle with the boardwalk.

The segment where the pedestrian crossing should be painted is a half-line, starting at the corner and extending to the building parallel to the boardwalk.

Answer sheet:

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