Final answer:
Point A has coordinates –(3,4), and when reflected across various axes, its image coordinates are: across the y-axis (3,4), across the x-axis (–3,–4), and across the line y=x (4,3).
Step-by-step explanation:
The question asks about the coordinates of point A after it is reflected across different lines in the Cartesian coordinate system. When a point is reflected across the y-axis, its x-coordinate changes sign while the y-coordinate remains the same. When it is reflected across the x-axis, its y-coordinate changes sign while the x-coordinate remains the same. And when it is reflected across the line y=x, the x and y coordinates are swapped.
The point A has coordinates –(3,4). When A is reflected across the y-axis, its image has coordinates (3,4). When A is reflected across the x-axis, its image has coordinates (–3,–4). Finally, when A is reflected across the line y=x, its image has coordinates (4,3).
Therefore, the correct answer is: A. (3,4); (–3,–4); (4,3)