To determine the translation from quadrilateral ABCD to quadrilateral EFGH, we need to compare the coordinates of corresponding points before and after the translation.
Coordinates of quadrilateral ABCD:
- Point A: (2, 2)
- Point B: (6, 4)
- Point C: (10, 4)
- Point D: (6, 2)
Coordinates of quadrilateral EFGH:
- Point E: (11, -1)
- Point F: (15, -1)
- Point G: (19, 1)
- Point H: (15, 1)
Next, we'll find the translation for point A to point E as it helps to understand the translation for other points as well:
- For Point A to Point E:
- Change in x: 11 - 2 = 9 units to the right
- Change in y: -1 - 2 = -3 units down
Now, let's check if the same translation applies to the other points:
-
Point B to Point F:
- Change in x: 15 - 6 = 9 units to the right
- Change in y: -1 - 4 = -5 units down (not consistent)
-
Point C to Point G:
- Change in x: 19 - 10 = 9 units to the right
- Change in y: 1 - 4 = -3 units down (consistent)
-
Point D to Point H:
- Change in x: 15 - 6 = 9 units to the right
- Change in y: 1 - 2 = -1 unit down (not consistent)
From the calculations:
- Point A, C have consistent changes of 9 units to the right and -3 units down.
- Point B has a different downward change.
- Point D also has a different downward change.
Since the movement from A to E and C to G can be seen as a consistent translation of 9 units to the right and 2 units down (the average vertical translation between consistent pairs).
Thus, combining the results:
Quadrilateral ABCD has been translated 9 units to the right and approximately 3 units down on average with some inconsistencies on points B and D.
So, the translation can be summarized as:
Quadrilateral ABCD has been translated 9 units to the right and approximately 3 units down.
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