Co-ordinates Problem -- Expert advice would be appreciated

[knight247]

The OA is A

When I solve the problem in the way I'm most familiar with, I get A and C as the right answers, and I'm simply not able to solve any further and choose between those two options. The explanation provided is not detailed enough to understand.

I hope to get some expert advice on this. Detailed explanations would be appreciated. Thank you.

[GMATGuruNY]

LOOK AT THE ANSWER CHOICES AND DRAW.



The figure above shows the following:
(2,6) is closer to B than to O. Eliminate D.
(2,-6) is closer to O than to B. Eliminate C.
(0,4) and (4,0) each imply that OAB is a 45-45-90 triangle with a base and height of 4. Since the resulting area would be less than 16, eliminate B and E.

The correct answer is A.