MathDB

Let

S

be the set of 81 points

(x, y)

such that

x

and

y

are integers from

-4

through

4

. Let

A

B

, and

C

be random points chosen independently from

S

, with each of the 81 points being equally likely. (The points

A

B

, and

C

do not have to be different.) Let

K

be the area of the (possibly degenerate) triangle

ABC

. What is the expected value (average value) of

K^2

19