In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (5,5) 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.  Answers: 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 (0,5) or (5,0), then the area is 1/2*5*5=25/2. Thus A must be at (2,6).   Answer: (2,6).
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In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (5,5) 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.