Final answer:
The coordinates of the reflected image of a point depend upon the line it is being reflected across. Without specific details on the line, we can only discuss general methods of reflection across common lines like the x-axis, y-axis, y=x, and y=-x.
Step-by-step explanation:
The question is asking to find the coordinates of the image of a point when reflected across different lines. For the point (-1, -4), without details on which specific lines we need to reflect across, we can only discuss the general process of reflection across some common lines like the x-axis, y-axis, y=x, y=-x, or any arbitrary line y=mx+b. To reflect a point across a line, one typically applies specific rules or formulas which involve changing the sign of one or both coordinates, or finding the perpendicular from the point to the line and then using similar triangles to locate the image on the opposite side of the line.
For example, reflecting the point (-1, -4) across the x-axis would invert the y-coordinate, resulting in the point (-1, 4). Reflection across the y-axis would invert the x-coordinate, giving us (1, -4). Reflection across the line y=x would switch the x and y coordinates, resulting in (-4, -1). However, without specific lines to reflect across mentioned in the question, we can't give an exact answer.
In cases involving mirrors such as concave mirrors or specific arrangements like parallel mirrors, ray diagrams and the principles of optics would be used to locate the image(s).