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.
To calculate the point that is equidistant from all three gates, Lisa, Bree, and Caleb should follow these steps:
1. Locate the gates on the amusement park map. Assume that the gates are labeled as Gate A, Gate B, and Gate C.
2. Using a ruler or a compass, draw a line segment that represents the distance between Gate A and Gate B. Mark the midpoint of this line segment as point M. Repeat this step to find the midpoint between Gate B and Gate C, marking it as point N.
3. Draw a line perpendicular to the line segment MN, passing through the midpoint M. This line will intersect the line segment AB at point X. Repeat this step to find the intersection of the perpendicular line and line segment BC, marking it as point Y.
4. Draw a line perpendicular to the line segment MY, passing through the midpoint N. This line will intersect the line segment AC at point Z.
5. The intersection of lines XZ and MY is the point that is equidistant from all three gates (Gate A, Gate B, and Gate C).
By following these steps, Lisa, Bree, and Caleb will be able to calculate the point that is equidistant from all three gates on the amusement park diagram.