To determine the translation of quadrilateral ABCD to quadrilateral HEGF, we can analyze the original coordinates of points A, B, C, and D, and the new coordinates of points H, E, G, and F.
The original points are:
- A(2, 2)
- B(4, 6)
- C(4, 10)
- D(2, 6)
The new points are:
- H(1, 15)
- E(11, 1)
- G(1, 19)
- F(15, 1)
To find how the translation has occurred, we subtract the original coordinates from the new coordinates. This will help us find the translation vector.
Let's take the point A(2, 2) and translate it to H(1, 15):
- For the x-coordinate: \(1 - 2 = -1\)
- For the y-coordinate: \(15 - 2 = 13\)
Thus, from A to H, the translation vector is (-1, 13).
Now, let's check the other points to see if the same vector applies:
-
For B(4, 6) to E(11, 1):
- \(11 - 4 = 7\) for x
- \(1 - 6 = -5\) for y
- Translation vector here is (7, -5).
-
For C(4, 10) to G(1, 19):
- \(1 - 4 = -3\) for x
- \(19 - 10 = 9\) for y
- Translation vector here is (-3, 9).
-
For D(2, 6) to F(15, 1):
- \(15 - 2 = 13\) for x
- \(1 - 6 = -5\) for y
- Translation vector here is (13, -5).
Since the translation vectors are not consistent among the points, it appears that the translation has not occurred uniformly. Different points do not have the same translation vector.
The translation must have involved a combination of translations or possibly a reflection or rotation, or the points may not have been correctly correlated.
Therefore, based simply on the provided information, no singular translation exists that matches all points from quadrilateral ABCD to HEGF.