Final Answer:
The coordinates of the vertices after the reflection across y = -x are obtained by switching the x and y coordinates and changing their signs.
Step-by-step explanation:
When a figure is reflected across a line, such as y = -x, the coordinates of its vertices are transformed. To find the new coordinates, we switch the x and y coordinates and change their signs.
For example, if a vertex has original coordinates (x, y), after the reflection, its new coordinates will be (-y, -x).
This transformation can be applied to each vertex of the figure. By switching the x and y coordinates and changing their signs, we obtain the new coordinates of the vertices after the reflection across y = -x.
It is important to note that the line y = -x acts as the mirror line for the reflection. The vertices on one side of the line will be mapped to the other side, maintaining the same distance from the mirror line.
By performing this transformation on each vertex, we can determine the new coordinates of the vertices after the reflection.
In conclusion, to find the coordinates of the vertices after the reflection across y = -x, we switch the x and y coordinates and change their signs. This transformation allows us to obtain the new positions of the vertices, reflecting the figure across the given line.