Question

Let A1, A2,…. An be n points in plane. For each subset Ai,

Ai2,…..Aik we call the centroid of Ai, Ai2,…. Aik a point Gi,…. ik
such that OGi….ik =(OAi+…..+OAik)/k
Show that the centroi of A

Answer 1

The centroid of a subset of points in the plane can be found by taking the average of the x-coordinates and the average of the y-coordinates of the points in the subset.

Step-by-step explanation:

The centroid is a point that represents the center of mass or balance of a geometric figure. In this case, we have n points in the plane represented by A1, A2,..., An. To find the centroid of a subset Ai, Ai2,..., Aik, we need to find the average of the x-coordinates and the average of the y-coordinates of all the points in the subset. This can be expressed as:

G = (1/k) * (A1 + A2 + ... + Aik)

For example, if we have three points A1(1, 4), A2(3, 2), and A3(5, 6), we can find the centroid of the subset A1, A2, A3 as:

1. Average of x-coordinates: (1 + 3 + 5) / 3 = 3
2. Average of y-coordinates: (4 + 2 + 6) / 3 = 4
3. The centroid of A1, A2, A3: G = (3, 4)