Transformation involves changing the position of a shape.
The sequence of transformation is: (d) A translation rule by [tex]\mathbf{(x,y) \to (x, y - 9)}[/tex] and then a 180 degrees clockwise rotation about the origin
The coordinates of the pre-image is:
[tex]\mathbf{A = (2,3)}[/tex]
[tex]\mathbf{B = (5,6)}[/tex]
[tex]\mathbf{C = (8,6)}[/tex]
[tex]\mathbf{D = (8,3)}[/tex]
Of the given sequence of transformations, option (d) is correct.
The proof is as follows.
First, translate ABCD by (x, y - 9)
So, we have:
[tex]\mathbf{(x,y) \to (x, y - 9)}[/tex]
[tex]\mathbf{(2,3) \to (2, -6)}[/tex]
[tex]\mathbf{(5,6) \to (5, -3)}[/tex]
[tex]\mathbf{(8,6) \to (8, -3)}[/tex]
[tex]\mathbf{(8,3) \to (8, -6)}[/tex]
Next, rotate by 180 degrees.
The rule of this transformation is:
[tex]\mathbf{(x,y) \to (-x,-y)}[/tex]
So, we have:
[tex]\mathbf{(2,-6) \to (-2,6)}[/tex]
[tex]\mathbf{(5,-3) \to (-5,3)}[/tex]
[tex]\mathbf{(8,-3) \to (-8,3)}[/tex]
[tex]\mathbf{(8,-6) \to (-8,6)}[/tex]
From the graph, the coordinates of the image are:
[tex]\mathbf{A" = (-2, 6)}[/tex]
[tex]\mathbf{ B" = (-5,3)}[/tex]
[tex]\mathbf{C" = (-8,3)}[/tex]
[tex]\mathbf{D" = (-8,6)}[/tex]
Hence, the sequence of transformation is:
(d) A translation rule by [tex]\mathbf{(x,y) \to (x, y - 9)}[/tex] and then a 180 degrees clockwise rotation about the origin
Read more about transformations at:
https://brainly.com/question/11707700
