Translation of negative 6 units x, 1 units y composition reflection across the x-axis
The composition transformation that maps ABCD to A''B''C''D'' comprises
of two or more transformations that maps the image
The rule that describes the composition transformation that maps ABCD to
A''B''C''D'' is the option;
Translation of negative 6 units x, 1 units y composition reflection across the x-axis.
The given coordinates of parallelogram ABCD are (3, 5), (6, 5), (4, 1), (1, 1)
The coordinates of the parallelogram A'B'C'D' are; A'(3, -5), B'(6, -5), C'(4, -1), D(1, -1)
The coordinates of the parallelogram A''B''C''D'' are;
D(-5, 0), C''(-2, 0), A''(-3, -4), B''(0, -4)
The image of the point (x, y), following a reflection about the x-axis is the point (x, -y)
The difference in the coordinates of the parallelogram ABCD and A'B'C'D'
is the change in the sign of the y-coordinates
Therefore, the transformation that gives the parallelogram A'B'C'D' from
the parallelogram ABCD is a reflection about the x-axis
The difference between the coordinates of the vertices of the
parallelogram A'B'C'D' and the parallelogram A''B''C''D'', is a change in the
x-value by (-6), and a change in the y-value by (+1)
Therefore, the parallelogram A''B''C''D'' can be obtained from parallelogram
A'B'C'D', by a translation of -6 units (left) in the x-direction and a translation
of 1 unit, x in the y-direction
Which gives;
The composition transformation that maps the pre-image ABCD to the
final image A''B''C''D'', (given that in a composition transformation, the
transformation to the right is done first) are;
which is the option;
Translation of negative 6 units x, 1 units y composition reflection across the x-axis
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