In the rectangular coordinate system above, if point \(A\) (not shown) is equidistant from points \(O\) and \(B\) and

[Vincen]

In the rectangular coordinate system above, if point \(A\) (not shown) is equidistant from points \(O\) and \(B\) and the area of triangle \(OAB\) is \(16,\) which of the following are the possible coordinates of point \(A?\)

A. \((-2, 6)\)
B. \((0, 4)\)
C. \((2, -6)\)
D. \((2, 6)\)
E. \((4, 0)\)

Answer: A

Source: Manhattan GMAT