To find the units of translation for quadrilateral ABCD from its original coordinates (A(2,2), B(4,6), C(4,10), D(2,6)) to the new coordinates (H(1,15), E(11,1), G(1,19), F(15,1)), we can first analyze the transformation for one of the points.
Let's take the point A(2,2) and see where it maps to in the new coordinates.
Assuming A translates to H:
- Original point A = (2, 2)
- New point H = (1, 15)
Now, to find the translation:
-
Translation to the right (horizontal shift):
- The change in the x-coordinate: 1 - 2 = -1 (which means it's moved 1 unit to the left).
-
Translation down (vertical shift):
- The change in the y-coordinate: 15 - 2 = +13 (which means it's moved 13 units up).
So, point A translates 1 unit to the left and 13 units up.
Let's apply this to another point, for example, B(4,6) and see where it translates to:
Assuming B translates to E:
- Original point B = (4, 6)
- New point E = (11, 1)
Now, for point B to E:
-
Translation to the right:
- The change in the x-coordinate: 11 - 4 = 7 (which means moved 7 units to the right).
-
Translation down:
- The change in the y-coordinate: 1 - 6 = -5 (which means it's moved 5 units down).
Now, if we compare the translations from point A and point B, it seems that the translation is not consistent for all points, suggesting the quadrilateral has not uniformly translated in the same direction.
To summarize, quadrilateral ABCD has undergone a translation based on the points you provided, but since the translations appear to differ among points, it is not a standard translation. Please clarify if there are any specific points you would like to use for the explanation or if you have any additional context.