The rule that describes the composition of transformations that maps δabc to δa"b"c" is reflection across the x-axis composition translation of negative 6 units x, negative 2 units y.
The single transformation that maps a onto c is the reflection of the triangle a about the line y = -x
To answer the question, we note that the result of reflection of a point (x, y) across the x axis is given as follows;
Coordinates before reflection = (x, y), Coordinates after reflection = (x, -y)
Also, when we rotate a point, (x, y), 90° clockwise, we have;
Image point before 90° clockwise rotation = (x, y), Image point after 90° clockwise rotation = (y, -x)
Therefore, the rotation of the point (x, -y), 90° clockwise will give,
Image point before 90° clockwise rotation = (x, -y), Image point after 90° clockwise rotation = (-y, -x)
Which gives the combined transformation as (x, y) → (-y, -x) which is the rule equivalent to reflection about the line y = -x.
The rule which describes the composition of transformations that maps δabc to δa"b"c" is need to be determine.
According to the reflection rule;
Reflection over the x-axis: (x,y)→(x,-y)
Also there is a translation according to the translation rule: translation (x,y)→(x-6,y-2)
Therefore, the rule that describes the composition of transformations that maps δabc to δa"b"c" is reflection across the x-axis composition translation of negative 6 units x, negative 2 units y.
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