Final answer:
The new coordinates after reflecting triangle ABC across the x-axis are A'(4,-6), B'(1,-1), and C'(4,-1), with the y-coordinates negated and the x-coordinates unchanged.
Step-by-step explanation:
When reflecting triangle ABC across the x-axis, the x-coordinates of the points will remain the same while the y-coordinates will become their opposite values. The new coordinates for point A(4,6) will be A'(4,-6), for point B(1,1) will be B'(1,-1), and for point C(4,1) will be C'(4,-1). A reflection across the x-axis changes the sign of the y-coordinate while maintaining the x-coordinate.