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
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40% (01:29) correct 
