In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (6,6) 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.
Options:
A) (-2,6)  B) (0,4)  C) (2,-6)  D) (2,6)  E) (4,8)
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 (0,6) or (6,0), then the area is 1/2*6*6= 
<gadget id="calculator">1/2*6*6</gadget>
<output>18</output>
18. Thus A must be at (4,8).   Answer: (4,8).
<result>E</result>
In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (6,6) 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.