To find out how much quadrilateral ABCD has been translated, we need to compare the original coordinates of points A, B, C, and D with the new coordinates of points H, E, G, and F.
The original coordinates are:
- A(2, 2)
- B(4, 6)
- C(4, 10)
- D(2, 6)
The new coordinates are:
- H(1, 15)
- E(11, 1)
- G(1, 19)
- F(15, 1)
To determine the translation, we will look at the coordinates of a pair of corresponding points. Let's match point A(2, 2) with point H(1, 15):
-
For the x-coordinates:
- Translation in the x-direction: 1 - 2 = -1 (translated 1 unit to the left)
-
For the y-coordinates:
- Translation in the y-direction: 15 - 2 = 13 (translated 13 units up)
From this analysis, it appears that quadrilateral ABCD has been translated 1 unit to the left and 13 units up.
We should perform similar steps for another point (for example, point B(4, 6) to E(11, 1)) to verify the translation remains consistent or to find the actual translation:
- For B(4, 6) to E(11, 1):
- Translation in the x-direction: 11 - 4 = 7 (translated 7 units to the right)
- Translation in the y-direction: 1 - 6 = -5 (translated 5 units down)
This gives inconsistent results, demonstrating that it’s unclear from the transformation or some of the points may not correspond correctly.
Let’s take another look for consistency: For points C(4,10) to G(1,19):
- For the x-coordinates:
- 1 - 4 = -3 (3 units to the left)
- For the y-coordinates:
- 19 - 10 = 9 (9 units up)
Summarizing from the observations above, the inconsistencies indicate that the provided new coordinates do not appear to effectively result from a simple translation of quadrilateral ABCD.
If we assume the coordinates are swapped or mismatched—it would require a re-examination of the specified translation or confirming the coordinates themselves.
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