To determine the translation applied to quadrilateral ABCD to get to the translated quadrilateral A'B'C'D', we will find the translation vector by comparing the coordinates of the original points (A, B, C, D) with the corresponding translated points (A', B', C', D').
- Calculate the translation for each point:
-
For point A(2, 2) to A'(11, -1):
- Translation in the x-direction: \( 11 - 2 = 9 \)
- Translation in the y-direction: \( -1 - 2 = -3 \)
-
For point B(6, 4) to B'(15, 1):
- Translation in the x-direction: \( 15 - 6 = 9 \)
- Translation in the y-direction: \( 1 - 4 = -3 \)
-
For point C(10, 4) to C'(10, 4):
- Translation in the x-direction: \( 10 - 10 = 0 \)
- Translation in the y-direction: \( 4 - 4 = 0 \)
-
For point D(6, 2) to D'(15, -1):
- Translation in the x-direction: \( 15 - 6 = 9 \)
- Translation in the y-direction: \( -1 - 2 = -3 \)
- Summarizing the results, we see that points A, B, and D are all translated by \(9\) units to the right and \(3\) units down, while point C remains unchanged.
Final answer:
Quadrilateral ABCD has been translated 9 units to the right and 3 units down.