In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (4,3) and if point A is equidistant from points O and B and the area of the triangle OAB is 16, which of the following are the possible coordinates of point A.
Select the correct option.
A) (-2,6)
B) (0,4)
C) (2,-6)
D) (2,6)
E) (4,0)
Area.pngSince A is equidistant from points O and B, then it must be somewhere on the green line (perpendicular bisector of OB).   (2,-6) and (2,6) are not on that line. If A is at (0,4) or (3,0), then the area is 1/2*4*3= 
<gadget id="calculator">1/2*4*3</gadget>
<output>6</output>
6. Thus A must be at (2,-6).   Answer: (2,-6).
<result>C</result>
In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (4,3) and if point A is equidistant from points O and B and the area of the triangle OAB is 16, which of the following are the possible coordinates of point A.