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Question about Lines, Line Segments, and Rays

Mathematics

Originais Teachy

Lines, Line Segments, and Rays

Hard

(Originais Teachy 2024) - Question Hard of Mathematics

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.
a.
With the information provided in the statement, it is not possible to determine the exact position of the tourist attraction point XYZ in relation to the intersection of streets A and B.
b.
The point XYZ is located at coordinates (-x, y), where x and y are negative positions of A and B, respectively.

Answer sheet:

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