Given: AD = BC and AD || BC Prove: ABCD is a parallelogram.
2 answers:
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Answer:
The sequence of transformations involved is a reflection across the x axis, followed by a reflection across the y = x line
Step-by-step explanation:
The polygon ABCD is shown in the image attached. The coordinates of the polygon are A(-6, 6), B(-4, 6), C(-4, 4), D(-6, 2), while the polygon A'B'C'D' is at A'(-6, -6), B'(-6, -4), C'(-4, -4), D'(-2, -6)
A transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, dilation and rotation.
If a point O(x, y) is reflected across the x axis, the new coordinate is O'(x, -y).
If a point O(x, y) is reflected across the y = x line, the new coordinate is O'(y, x)
Hence if polygon ABCD is reflected across the x axis, the new coordinates are A*(-6, -6), B*(-4, -6), C*(-4, -4), D*(-6, -2). If a reflection across the y = x line, the new coordinates are A'(-6, -6), B'(-6, -4), C'(-4, -4), D'(-2, -6)
