Answer:
The two lines of reflection are [tex]x=-1[/tex] and [tex]y=2[/tex]
Step-by-step explanation:
I will attach a file with the graph of the rectangle and the lines of reflection.
We know that RSTU is a rectangle with vertices at [tex]R=(-3,1)[/tex] , [tex]S=(1,1)[/tex],
[tex]T=(-3,3)[/tex] and [tex]U=(1,3)[/tex]
The first step is to draw the vertices on the plane and them the rectangle.
The rectangle is a symmetrical figure. Therefore if we want to carry the rectangle onto itself using a line of reflection this line must goes through the centroid of the rectangle.
Given that we have a rectangle whose width is [tex]a[/tex] and its length is [tex]b[/tex] its centroid will be place at [tex](\frac{a}{2},\frac{b}{2})[/tex].
Looking at the graph and using this information we find that the two lines of reflection are [tex]x=-1[/tex] and [tex]y=2[/tex].
