Find the glide reflection image of the black triangle where the translation is (x,y) ---> (x,y - 7) and line of reflection is x - 1
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Transformation involves changing the position of a shape.
The image of the black triangle is option (d)
The coordinates of the black triangle are:
[tex]\mathbf{A = (2,8)}[/tex]
[tex]\mathbf{B = (2,5)}[/tex]
[tex]\mathbf{C = (5,5)}[/tex]
When the triangle is transformed by [tex]\mathbf{(x,y) \to (x,y - 7)}[/tex]
The new coordinates are:
[tex]\mathbf{A' = (2,8 - 7) = (2,1)}[/tex]
[tex]\mathbf{B' = (2,5 - 7) = (2,-2)}[/tex]
[tex]\mathbf{C' = (5,5 - 7) = (5,-2)}[/tex]
When the triangle is reflected across the line [tex]\mathbf{x = 1}[/tex]
The rule of transformation is:
[tex]\mathbf{(x,y) \to (-(x - 2),y)}[/tex]
So, we have:
[tex]\mathbf{A" = (-(2 - 2),1) = (0,1)}[/tex]
[tex]\mathbf{B" = (-(2 - 2),-2) = (0,-2)}[/tex]
[tex]\mathbf{C" = (-(5 - 2),-2) = (-3,-2)}[/tex]
So, the coordinates of the image of the triangle are:
[tex]\mathbf{A" = (0,1)}[/tex]
[tex]\mathbf{B" =(0,-2)}[/tex]
[tex]\mathbf{C" = (-3,-2)}[/tex]
The above coordinates are illustrated by the option (d)
Read more about transformations at:
https://brainly.com/question/11707700