Final answer:
The student's question is about translations and reflections in a coordinate system. The transformations given result in points being moved horizontally or vertically, or reflected over the x-axis or y-axis. The line of reflection for the transformations (x, y) -> (-x, y) and (x, y) -> (x, -y) are the y-axis and x-axis, respectively.
Step-by-step explanation:
The student is asking about various transformations in the coordinate system and the result of applying those transformations to specific points. The coordinate system is based on two perpendicular lines known as axes (the x-axis and y-axis), and it can be used to graph points and lines on a flat surface. When discussing translations such as Left 1, Up 3, we are essentially describing the movement of points in this coordinate space.
Using the given points (3, 2), (-3, -2), and (1, -4), transformations such as (x, y) -> (-x, y) and (x, y) -> (x, -y) will result in reflections over the y-axis and x-axis, respectively. For example, reflecting point (3, 2) over the y-axis using the rule (x, y) -> (-x, y) will result in the point (-3, 2). Similarly, reflecting the same point over the x-axis using the rule (x, y) -> (x, -y) will result in the point (3, -2).
The lines of reflection for the transformations (x, y) -> (-x, y) and (x, y) -> (x, -y) correspond to the y-axis and x-axis, respectively. Therefore, if we graph the points after applying the reflections, we can see that the original points are mirrored across these axes.