# One event at this year’s Battle of the Classes will be a pie-eating contest between the sophomores, juniors, and seniors. Five members of each class will be positioned on the football field at the points indicated below. At the whistle, one student from each class will run to the pie table, eat exactly one pie, and run back to his or her group. The next student will then repeat the process. The first class to eat five pies and return to home base will be the winner of the pie-eating contest. Where should the pie table be located so that it will be a fair contest? Explain your reasoning.

If we want the pie-eating contest to be totally impartial, we need to make sure the pie table is situated at an equal distance from all three classes. To achieve this, we can use the centroid of the triangle formed by the classes as the ideal location for the pie table. A triangle is a closed shape with three straight sides and angles, which is a basic figure in mathematics with many properties and measurements. There are different ways to classify triangles based on their sides and angles, and they have important applications in various fields like physics, engineering, calculus, and trigonometry. To determine the centroid of the triangle, we can calculate the average of the x-coordinates and the y-coordinates of the three points (A, B, and C), which gives us the center of mass of the triangle. We can denote this point as G, and its coordinates are found by using the following formula: xG = (xA + xB + xC) / 3 yG = (yA + yB + yC) / 3 Once we have the coordinates of the centroid, we can place the pie table at this location, and all three classes will have to cover the same distance to reach the table and go back to their starting point. In summary, to ensure a fair competition, we should place the pie table at the centroid of the triangle formed by the three classes. If you want to learn more about triangles, you can follow this link: brainly.com/question/2773823 #SPJ1.