Final answer:
To find the geometric center of the given set of points, calculate the average of the x-coordinates and y-coordinates, and use these averages to determine the center's coordinates.
Step-by-step explanation:
The correct answer is to find the geometric center (also known as the centroid) for a set of points, you should calculate the average of the x-coordinates and the y-coordinates of all the points in the set. To do this, sum up all the x-coordinates and then divide by the number of points to find the average x-coordinate. Repeat this process for the y-coordinates to find the average y-coordinate.
In this specific case, to find the geometric center of the points x1 = (-14, 12), x2 = (-27, -3), x3 = (7, 2), x4 = (5, -10), x5 = (11, 0), and x6 = (6, 4), add up each set of coordinates separately (i.e., sum all x-coordinates together and all y-coordinates together), and then divide each sum by 6 (since there are 6 points).
Therefore, the geometric center will have the coordinates (x, y), where x = (-14 - 27 + 7 + 5 + 11 + 6) / 6 and y = (12 - 3 + 2 - 10 + 0 + 4) / 6.