Equidistance: Thunder and Lightening Part 2
If three people hear the same thunderclap simultaneously, where did the lightning strike?
- Plot three points A, B, and C to represent the location of 3 different people. Then plot point D to represent the point at which lightning strikes. Drag point D around to different locations. Is there a location where all three people could have heard thunder simultaneously? How many locations exist?
- Drag points A, B, and C around to different positions. Is it always possible to find a location for point D where all three people will hear thunder at the same time? Explain your reasoning.
- Using your knowledge of triangle centers, construct the center (incenter, circumcenter, orthocenter, or centroid) that would best model this situation. Show that the lightning strike is always equidistant from the three people using the measurement tool to display distances. (Note: you should label the point where the lightning is striking. It does not need to be point D as we had in steps 1 and 2).
- Show that the center you chose can model this scenario in any situation by dragging A, B, and C to various locations. What three scenarios stick out to you
- If a fourth person were to hear the same thunder clap at the same time as the people at point A, B, and C, where could they be located? Explain your reasoning.
Submit your answers and screenshots of your work from each step.