Transformation involves moving a point away from its original location.
The vertices of the pre-image are:
[tex]\mathbf{(-1,0)\ and\ (-1,-5)}[/tex]
The rule is given as:
[tex]\mathbf{r_{y=x} ^oT_{4,0(x,y)}}[/tex]
The above rule means that
ABCD was translated by 4 units to the right, then reflected over line y = x,
The rule of right translation by 4 units is:
[tex]\mathbf{(x,y) \to (x + 4,y)}[/tex]
The rule of reflection over [tex]\mathbf{y = x}[/tex] is:
[tex]\mathbf{(x,y) \to (y,x + 4)}[/tex]
The coordinates of A"B"C"D" are:
[tex]\mathbf{A" = (-4,5)}[/tex]
[tex]\mathbf{B" = (-1,5)}[/tex]
[tex]\mathbf{C" = (0,3)}[/tex]
[tex]\mathbf{D" = (-5,3)}[/tex]
So, we have:
[tex]\mathbf{(x,y) \to (y,x + 4)}[/tex] and [tex]\mathbf{A" = (-4,5)}[/tex]
[tex]\mathbf{y = -4}[/tex]
[tex]\mathbf{x + 4 = 5}[/tex]
[tex]\mathbf{x = 1}[/tex]
This means:
[tex]\mathbf{A = (1,5)}[/tex]
[tex]\mathbf{(x,y) \to (y,x + 4)}[/tex] and [tex]\mathbf{B" = (-1,5)}[/tex]
[tex]\mathbf{y = -1}[/tex]
[tex]\mathbf{x + 4 = 5}[/tex]
[tex]\mathbf{x = 1}[/tex]
This means:
[tex]\mathbf{B = (1,-1)}[/tex]
[tex]\mathbf{(x,y) \to (y,x + 4)}[/tex] and [tex]\mathbf{C" = (0,3)}[/tex]
[tex]\mathbf{y = 0}[/tex]
[tex]\mathbf{x + 4 = 3}[/tex]
[tex]\mathbf{x = -1}[/tex]
This means:
[tex]\mathbf{C = (-1,0)}[/tex]
[tex]\mathbf{(x,y) \to (y,x + 4)}[/tex] and [tex]\mathbf{D" = (-5,3)}[/tex]
[tex]\mathbf{y = -5}[/tex]
[tex]\mathbf{x + 4 = 3}[/tex]
[tex]\mathbf{x = -1}[/tex]
This means:
[tex]\mathbf{D = (-1,-5)}[/tex]
Hence, the vertices of the pre-image are:
[tex]\mathbf{(-1,0)\ and\ (-1,-5)}[/tex]
Read more about transformation at:
https://brainly.com/question/13801312
