To find point J on line segment AB such that the ratio of AJ to JB is 1:1, we need to determine the midpoint of segment AB.
The coordinates of point A are (0,0) and the coordinates of point B are (0,6).
To find the midpoint J, we can use the midpoint formula: \[ J = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Substituting the coordinates of points A and B: \[ J = \left( \frac{0 + 0}{2}, \frac{0 + 6}{2} \right) = \left( 0, \frac{6}{2} \right) = (0, 3) \]
Thus, the coordinates of point J are (0, 3).
Therefore, the correct answer is: b. J (0,3).