Final answer:
The points B, C, and D are reflections of point A across the axes on the Cartesian coordinate system, with B across the x-axis, C across both axes, and D across the y-axis.
Step-by-step explanation:
The relationship between the given point A(5,3) and the points B(5,-3), C(-5,-3), and D(-5,3) can be described in terms of reflections across the axes in the Cartesian coordinate system. The point B(5,-3) is the reflection of point A across the x-axis, meaning the x-coordinate remains the same, while the y-coordinate is the negative of the original. Similarly, point C(-5,-3) is the reflection of point A across both the x-axis and y-axis, as both coordinates are the negatives of the original point's coordinates. Lastly, point D(-5,3) is the reflection of point A across the y-axis, where the x-coordinate is the negative while the y-coordinate remains the same.