In order to find the point that is equidistant from all three gates, Lisa, Bree, and Caleb need to locate the circumcenter of the triangle formed by their three respective entrances.
To do this, they can follow these steps:
1. Identify the exact locations of the three gates on the diagram of the park.
2. Draw lines to connect each pair of gates. This will create a triangle.
3. Use a ruler and a compass to find the midpoint of each side of the triangle. To do this, place the compass at one end of a side and draw an arc that intersects the midpoint of the opposite side. Repeat this process for the other two sides.
4. After finding the midpoints of each side, draw lines to connect each midpoint. These lines are called the perpendicular bisectors.
5. The point where all three perpendicular bisectors intersect is the circumcenter of the triangle. This point is equidistant from all three gates.
Note: Depending on the position and shape of the gates on the diagram, the circumcenter may be located inside or outside of the park.
Lisa, Bree, and Caleb are meeting at an amusement park. They each enter at a different gate. On this diagram of the park, explain how the friends could calculate the point that is equidistant from all three gates.
gates
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