Reflecting polygon ABCDE across the x-axis negates the x-coordinate (coordinates become (-x, y), and translating 4 units left adds 4 to the
x-coordinate. So, the combined transformation is (-x + 4, y).
The image shows a coordinate grid with two polygons, ABCDE and A'B'C'D'E'. Polygon ABCDE is reflected across the x-axis, then translated 4 units to the left. Therefore, the following series of transformations would map polygon ABCDE onto polygon A'B'C'D'E':
1. Reflection across the x-axis.
2. Translation 4 units to the left.
Mathematical description
Let the coordinates of point A in polygon ABCDE be (x, y). Then, the coordinates of point A' in polygon A'B'C'D'E' will be (-x, y).
The translation to the left can be described by the following vector:
[4, 0]
Therefore, the coordinates of point A' after the translation will be:
(-x, y) + [4, 0] = (-x + 4, y)
This is precisely the coordinates of point A' in polygon A'B'C'D'E'.
Conclusion
The following series of transformations would map polygon ABCDE onto polygon A'B'C'D'E':
1. Reflection across the x-axis.
2. Translation 4 units to the left.