The complete statement is:
The sequence of transformations that maps [tex]\triangle ABC[/tex] onto [tex]\triangle A'B'C'[/tex] is a
reflection across the line x=-3 followed by a reflection across the line y=x
The coordinates of triangle ABC are:
A= (-4,4), B = (-8,2) and C = (-6,6)
First, the triangle is reflected across the line x = -3.
The rule of this transformation is:
[tex](x,y) \to (|x| - 6,y)[/tex]
When the above transformation is applied to [tex]\triangle ABC[/tex], the coordinates become:
[tex]A = (-2,4)[/tex]
[tex]B = (2,2)[/tex]
[tex]C = (0,6)[/tex]
Next, reflect the above coordinates across the line y = x
The rule of this transformation is:
[tex](x,y) \to (y,x)[/tex]
When the above transformation is applied to [tex]\triangle ABC[/tex], the coordinates become:
[tex]A' = (4,-2)[/tex]
[tex]B' = (2,2)[/tex]
[tex]C' = (6,0)[/tex]
Hence, the sequence of transformations that maps [tex]\triangle ABC[/tex] onto [tex]\triangle A'B'C'[/tex] is a reflection across the line x=-3 followed by a reflection across the line y=x
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