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