Question
Figure TUVW is transformed to T′U′V′W′, as shown:
A coordinate plane is shown. Figure TUVW has vertices T at 3 comma negative 4, U at 4 comma negative 2, V at 6 comma negative 1 and W at 6 comma negative 4. Figure T prime U prime V prime W prime has vertices at T prime negative 5 comma negative 4, U prime at negative 6 comma negative 2, V prime at negative 8 comma negative 1, and W prime at negative 8 comma negative 4.
Which of the following sequences of transformations is used to obtain figure T′U′V′W′ from TUVW? (4 points)
A coordinate plane is shown. Figure TUVW has vertices T at 3 comma negative 4, U at 4 comma negative 2, V at 6 comma negative 1 and W at 6 comma negative 4. Figure T prime U prime V prime W prime has vertices at T prime negative 5 comma negative 4, U prime at negative 6 comma negative 2, V prime at negative 8 comma negative 1, and W prime at negative 8 comma negative 4.
Which of the following sequences of transformations is used to obtain figure T′U′V′W′ from TUVW? (4 points)
Answers
GPT 3.5
The given sequence of transformations can be determined by comparing the coordinates of the vertices of TUVW and T'U'V'W':
1. Translation: T => T'
The x-coordinate of T has changed from 3 to -5 (shifted left 8 units), and the y-coordinate remains the same.
2. Reflection: U => U'
The x-coordinate of U has changed from 4 to -6 (reflected over the y-axis), and the y-coordinate remains the same.
3. Translation: V => V'
The x-coordinate of V has changed from 6 to -8 (shifted left 14 units), and the y-coordinate remains the same.
4. No transformation: W => W'
The coordinates of W remain the same.
Therefore, the sequence of transformations used to obtain figure T'U'V'W' from TUVW is:
Translation (left 8 units), Reflection (over the y-axis), Translation (left 14 units), No transformation.
1. Translation: T => T'
The x-coordinate of T has changed from 3 to -5 (shifted left 8 units), and the y-coordinate remains the same.
2. Reflection: U => U'
The x-coordinate of U has changed from 4 to -6 (reflected over the y-axis), and the y-coordinate remains the same.
3. Translation: V => V'
The x-coordinate of V has changed from 6 to -8 (shifted left 14 units), and the y-coordinate remains the same.
4. No transformation: W => W'
The coordinates of W remain the same.
Therefore, the sequence of transformations used to obtain figure T'U'V'W' from TUVW is:
Translation (left 8 units), Reflection (over the y-axis), Translation (left 14 units), No transformation.