Question
What kind of translation has been done to quadrilateral ABCD if the coordinates for the earlier question are; A(2, 2), B(6, 4), C(10, 4), D(6, 2), AND a(11, -1), b(15, 1), c(19, 1), d(15, -1)?
Answers
GPT-4o mini
To determine the type of translation applied to quadrilateral ABCD given the original coordinates A(2, 2), B(6, 4), C(10, 4), D(6, 2) and the new coordinates a(11, -1), b(15, 1), c(19, 1), d(15, -1), we need to calculate the translation vector.
1. **Find the translation vector:**
To find the translation vector, we can subtract the coordinates of the original points from the corresponding new points.
For point A to point a:
\[
(11 - 2, -1 - 2) = (9, -3)
\]
For point B to point b:
\[
(15 - 6, 1 - 4) = (9, -3)
\]
For point C to point c:
\[
(19 - 10, 1 - 4) = (9, -3)
\]
For point D to point d:
\[
(15 - 6, -1 - 2) = (9, -3)
\]
2. **Conclusion:**
The translation vector for the transformation from ABCD to abcd is (9, -3). This means that each point of quadrilateral ABCD has been translated 9 units to the right and 3 units down to obtain the coordinates of quadrilateral abcd.
Thus, the translation done to quadrilateral ABCD is defined by the vector (9, -3).
1. **Find the translation vector:**
To find the translation vector, we can subtract the coordinates of the original points from the corresponding new points.
For point A to point a:
\[
(11 - 2, -1 - 2) = (9, -3)
\]
For point B to point b:
\[
(15 - 6, 1 - 4) = (9, -3)
\]
For point C to point c:
\[
(19 - 10, 1 - 4) = (9, -3)
\]
For point D to point d:
\[
(15 - 6, -1 - 2) = (9, -3)
\]
2. **Conclusion:**
The translation vector for the transformation from ABCD to abcd is (9, -3). This means that each point of quadrilateral ABCD has been translated 9 units to the right and 3 units down to obtain the coordinates of quadrilateral abcd.
Thus, the translation done to quadrilateral ABCD is defined by the vector (9, -3).