Lets use the determinant method to find out the area from the question stem.

Area of triangle = 1/2 |-1(1-y)-1(4-x) +1 (4y-x) = 1/2(y-1 = x-4 =4y-x) = (5y-5)/2 = 5 (y-1)/2

A=5(y-1)/2

Lets look at statement I and II

statement I)

y2-2y-3=0--> y2-3y+y-3 = 0 --> (y-3)(y+1) =0--> y=-1 or y=3

For y=(-1), A= 5/2(-1-1)= -5

For y=3, A=5/2(3-1)= +5

area is always positive , therefore for both cases area is same that is A=5 units

A is sufficient, so cancel out answer B,C,E; only possibilities are A and D

statement II)

x2=y2

x2-y2=0

(x+y)(x-y)=0

either x=-y or x=y

Area is dependent on value of y, since value of y is not defined on basis of a variable x, therefore statement II is not sufficient

Answer= A

_________________

GMAT chronicles : 670-->660--> 700--> 650--> 680-->660--> 610-->700 (main exam)-->710--740-->700 (main exam again) -->Target 740+

Never never never never NEVER give up!!

I can and I will- watch me.