Final answer:
To form a polygon with 8 distinct points on a plane, we need at least three points. We can choose any combination of 3, 4, 5, 6, 7, or all 8 points to form different polygons. The total number of polygons that can be formed is 219.
Step-by-step explanation:
To form a polygon, we need at least three points. Since we have 8 distinct points, we can choose any 3, 4, 5, 6, 7, or all 8 points to form different polygons. The total number of polygons that can be formed with 8 distinct points on a plane, no three of which are collinear, is given by the sum of binomial coefficients: C(8,3) + C(8,4) + C(8,5) + C(8,6) + C(8,7) + C(8,8). Calculating these binomial coefficients, we get the answer
Adding all these values, we have 56 + 70 + 56 + 28 + 8 + 1 = 219. Therefore, 219 polygons can be possibly formed from 8 distinct points on a plane.