To determine the translation that has been applied to the quadrilateral ABCD to obtain the new coordinates H, E, G, and F, we will calculate the changes in the x-coordinates and y-coordinates.
The original coordinates of the quadrilateral ABCD are:
- A(2, 2)
- B(4, 6)
- C(4, 10)
- D(2, 6)
The new coordinates after translation are:
- H(1, 15)
- E(11, 1)
- G(1, 19)
- F(15, 1)
To find out how much the quadrilateral has been translated, we compare the original coordinates and the new coordinates:
-
For point A(2, 2) to H(1, 15):
- Change in x: 1 - 2 = -1 (translated 1 unit to the left)
- Change in y: 15 - 2 = 13 (translated 13 units up)
-
For point B(4, 6) to E(11, 1):
- Change in x: 11 - 4 = 7 (translated 7 units to the right)
- Change in y: 1 - 6 = -5 (translated 5 units down)
-
For point C(4, 10) to G(1, 19):
- Change in x: 1 - 4 = -3 (translated 3 units to the left)
- Change in y: 19 - 10 = 9 (translated 9 units up)
-
For point D(2, 6) to F(15, 1):
- Change in x: 15 - 2 = 13 (translated 13 units to the right)
- Change in y: 1 - 6 = -5 (translated 5 units down)
After analyzing each point, we see that the translations are not consistent across corresponding points, which indicates the transformation is not a simple uniform translation of the entire shape.
Hence, the translation characteristics for the original quadrilateral ABCD do not yield a singular translation (same units to the right and down) when we compare each point. Therefore, it's confirmed that the original translation is more complex.
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