Question
What two rigid transformations were performed on figure ABCD
to produce the congruent figure WXYZ
?
(1 point)
Responses
ABCD
was first rotated −270°
(clockwise), then shifted 3 units to the left and 5 units up.
upper A upper B upper C upper D was first rotated negative 270 degrees (clockwise), then shifted 3 units to the left and 5 units up.
ABCD
was first rotated 90°
(counterclockwise), then shifted 3 units to the left and 5 units up.
upper A upper B upper C upper D was first rotated 90 degrees (counterclockwise), then shifted 3 units to the left and 5 units up.
ABCD
was first shifted 3 units to the left and 5 units up, then rotated −90°
(clockwise).
upper A upper B upper C upper D was first shifted 3 units to the left and 5 units up, then rotated negative 90 degrees (clockwise).
ABCD
was first shifted 3 units to the left and 5 units up, then rotated 90°
(counterclockwise).
to produce the congruent figure WXYZ
?
(1 point)
Responses
ABCD
was first rotated −270°
(clockwise), then shifted 3 units to the left and 5 units up.
upper A upper B upper C upper D was first rotated negative 270 degrees (clockwise), then shifted 3 units to the left and 5 units up.
ABCD
was first rotated 90°
(counterclockwise), then shifted 3 units to the left and 5 units up.
upper A upper B upper C upper D was first rotated 90 degrees (counterclockwise), then shifted 3 units to the left and 5 units up.
ABCD
was first shifted 3 units to the left and 5 units up, then rotated −90°
(clockwise).
upper A upper B upper C upper D was first shifted 3 units to the left and 5 units up, then rotated negative 90 degrees (clockwise).
ABCD
was first shifted 3 units to the left and 5 units up, then rotated 90°
(counterclockwise).
Answers
GPT-4o mini
To determine the correct sequence of rigid transformations that were performed on figure ABCD to produce the congruent figure WXYZ, we need to analyze the options given.
1. **Rotating -270° (clockwise)** is equivalent to rotating 90° (counterclockwise). This means that the rotation does not change the relative positions of the vertices besides rotating their orientation.
2. **Shifting (translating)** by 3 units to the left and 5 units up simply moves the entire figure without altering its shape or size.
Understanding this, let's analyze the provided options:
- The first option states that ABCD was first rotated -270° (clockwise), then shifted 3 units to the left and 5 units up. This means that the figure is rotated first, then translated.
- The second option states that ABCD was first rotated 90° (counterclockwise) and then shifted 3 units left and 5 units up. This is essentially the same transformation as the first but framed differently.
- The third option states that ABCD was first shifted and then rotated -90° (clockwise). This is a different sequence and might produce a different end position, depending on the original orientation.
- The last option mentions shifting ABCD first and then rotating 90° (counterclockwise), which may also lead to different positioning.
Given we know that the rotation is more of a redirection of orientation, the first two options (which essentially carry out the same transformations) are likely correct sequences.
Without additional visual information about the figures and their orientation, both the **first option** (rotating -270° then shifting) and the **second option** (rotating 90° then shifting) could be correct. However, since they convey the same operation but in different wording, the first option appears to make the transformations clearer by stating rotation first.
Thus, the best answer is:
**ABCD was first rotated -270° (clockwise), then shifted 3 units to the left and 5 units up.**
1. **Rotating -270° (clockwise)** is equivalent to rotating 90° (counterclockwise). This means that the rotation does not change the relative positions of the vertices besides rotating their orientation.
2. **Shifting (translating)** by 3 units to the left and 5 units up simply moves the entire figure without altering its shape or size.
Understanding this, let's analyze the provided options:
- The first option states that ABCD was first rotated -270° (clockwise), then shifted 3 units to the left and 5 units up. This means that the figure is rotated first, then translated.
- The second option states that ABCD was first rotated 90° (counterclockwise) and then shifted 3 units left and 5 units up. This is essentially the same transformation as the first but framed differently.
- The third option states that ABCD was first shifted and then rotated -90° (clockwise). This is a different sequence and might produce a different end position, depending on the original orientation.
- The last option mentions shifting ABCD first and then rotating 90° (counterclockwise), which may also lead to different positioning.
Given we know that the rotation is more of a redirection of orientation, the first two options (which essentially carry out the same transformations) are likely correct sequences.
Without additional visual information about the figures and their orientation, both the **first option** (rotating -270° then shifting) and the **second option** (rotating 90° then shifting) could be correct. However, since they convey the same operation but in different wording, the first option appears to make the transformations clearer by stating rotation first.
Thus, the best answer is:
**ABCD was first rotated -270° (clockwise), then shifted 3 units to the left and 5 units up.**