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 need to find the circumcenter of the triangle formed by their respective gates.
Let's assume the amusement park is represented by a simple diagram with three gates, labeled as Gate A, Gate B, and Gate C. These gates are connected by lines to form a triangle.
To start, Lisa, Bree, and Caleb can each locate their respective gates on the diagram. Then, they need to draw the line segments connecting the midpoints of the sides of the triangle. These lines are called the medians.
To find the midpoint of a side, they can divide the side into two equal parts and mark the halfway point. They need to do this for each side of the triangle.
Next, Lisa, Bree, and Caleb should connect the midpoint of one side to the opposite vertex, forming a line segment called a median. They will have three medians, one for each side of the triangle.
Finally, they need to locate the point where all three medians intersect. This point is known as the circumcenter and is equidistant from all three gates. It represents the point that is equidistant from their original positions in the amusement park.
Once they find this point, they can mark it on the diagram, and that is the point that is equidistant from all three gates.