I did this somewhat less elegantly than Anurag did. I recognized that the slope from (0,0) to (2,-2) is -1. I also recognized that the slope from (0,0) to (1,1) is 1. Since these are the negative reciprocals of each other, I saw that the lines were perpendicular, indicating a right triangle.
Then I used the formula Area = (1/2)*base*height, using the line from (0,0) to (2.-2) as the base, and the line from (0,0) to (1,1) as the height.
Length of (0,0) to (1,1) = square root of 2.
Length of (0,0) to (2,-2) = 2 * square root of 2
(1/2)*base*height = (1/2)*(2 * square root of 2)* (square root of 2) = 2.
I'm really old, but I'll never be too old to become more educated.
