On the Line 1 Copyright © 2026 Pearson Education, Inc. On the Line An amusement park has two main entrances. The maintenance team is placing a new digital information kiosk between the entrances. On a coordinate map of the park, Entrance A is located at (2, 6) and Entrance B is located at (8, 12). The maintenance team is considering two options: • Option 1: Place the kiosk midway between the two entrances. • Option 2: Place the kiosk closer to Entrance A, which receives twice as much traffic as Entrance B. To decide the best location, the team calculates both the midpoint and the weighted average and considers which location better serves the amusement park. 1. Plot Entrance A and Entrance B on the coordinate plane. 2. Determine the midpoint between Entrance A and Entrance B. Plot the midpoint on the coordinate plane. 3. Determine the weighted average of Entrance A and Entrance B. Use a weight of 2 for Entrance A and 1 for Entrance B, or the ratio A : B = 2 : 1. Plot the weighted average on the coordinate plane. 4. Which point, the midpoint or weighted average, is closer to Entrance A? Use the distance formula to support your answer. Show your work and explain your reasoning using precise math language.
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