Answer:
B. [tex](3,-1)[/tex]
Step-by-step explanation:
We have been given an image of a quadrilateral. We are asked to find the coordinates of the image of vertex F after a reflection across the line [tex]y=-x[/tex].
We know that rule of reflection across the line [tex]y=-x[/tex] is [tex](x,y)\rightarrow(-y,-x)[/tex].
We can see that coordinates of point F are [tex](1,-3)[/tex].
After reflecting point F across the line [tex]y=-x[/tex], the x- and y-coordinates will interchange their place and their signs will be changed as well.
[tex](1,-3)\rightarrow(--3,-1)=(3,-1)[/tex]
Therefore, the coordinates of the image of vertex F after a reflection across the line [tex]y=-x[/tex] are [tex](3,-1)[/tex] and option B is the correct choice.
