Lisa, Bree,and Caleb are meeting at an amusement park. They each enter at a different gate. 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 can follow these steps:
1. Determine the exact location of each gate in terms of coordinates on a map or in mathematical terms (e.g., Gate A is located at (x1, y1), Gate B is located at (x2, y2), and Gate C is located at (x3, y3)).
2. Use the distance formula (d = √((x2-x1)² + (y2-y1)²)) to calculate the distance between Gate A and Gate B, Gate B and Gate C, and Gate C and Gate A. This will result in three distance measurements: d1, d2, and d3.
3. Calculate the centroid of the three gates, which represents the point equidistant from all three gates. To do this, add up the x-coordinates of the gates and divide by 3 to find the average x-coordinate. Similarly, add up the y-coordinates and divide by 3 to find the average y-coordinate.
Centroid x-coordinate = (x1 + x2 + x3) / 3
Centroid y-coordinate = (y1 + y2 + y3) / 3
4. The calculated (x, y) coordinates of the centroid will represent the point that is equidistant from all three gates. This point will be the meeting point for Lisa, Bree, and Caleb at the amusement park.