Question
Question
Use the image to answer the question.
Two quadrilaterals, upper A upper B upper C upper D and upper W upper X upper Y upper Z, are graphed on a coordinate plane. The x axis ranges from negative 10 to 10 in increments of 1. The y axis ranges from negative 10 to 10 in increments of 1.
Image Long DescriptionPoint upper A has coordinates left parenthesis negative 6 comma negative 3 right parenthesis. Point upper B has coordinates left parenthesis negative 6 comma negative 5 right parenthesis. Point upper C has coordinates left parenthesis negative 4 comma negative 6 right parenthesis. Point upper D has coordinates left parenthesis negative 3 comma negative 2 right parenthesis. Point upper W has coordinates left parenthesis 2 comma 9 right parenthesis. Point upper X has coordinates left parenthesis 0 comma 9 right parenthesis. Point upper Y has coordinates left parenthesis negative 1 comma 7 right parenthesis. Point upper Z has coordinates left parenthesis 3 comma 6 right parenthesis.
What two rigid transformations were performed on figure ABCD
to produce the congruent figure WXYZ
?
(1 point)
Responses
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°
(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 (90 degrees clockwise).
ABCD
was first shifted 3 units to the left and 5 units up, then rotated 90°
(counterclockwise).
upper A upper B upper C upper D was first shifted 3 units to the left and 5 units up, then rotated 90 degrees (counterclockwise).
ABCD
was first rotated −270°
(270°
clockwise), then shifted 3 units to the left and 5 units up.
Use the image to answer the question.
Two quadrilaterals, upper A upper B upper C upper D and upper W upper X upper Y upper Z, are graphed on a coordinate plane. The x axis ranges from negative 10 to 10 in increments of 1. The y axis ranges from negative 10 to 10 in increments of 1.
Image Long DescriptionPoint upper A has coordinates left parenthesis negative 6 comma negative 3 right parenthesis. Point upper B has coordinates left parenthesis negative 6 comma negative 5 right parenthesis. Point upper C has coordinates left parenthesis negative 4 comma negative 6 right parenthesis. Point upper D has coordinates left parenthesis negative 3 comma negative 2 right parenthesis. Point upper W has coordinates left parenthesis 2 comma 9 right parenthesis. Point upper X has coordinates left parenthesis 0 comma 9 right parenthesis. Point upper Y has coordinates left parenthesis negative 1 comma 7 right parenthesis. Point upper Z has coordinates left parenthesis 3 comma 6 right parenthesis.
What two rigid transformations were performed on figure ABCD
to produce the congruent figure WXYZ
?
(1 point)
Responses
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°
(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 (90 degrees clockwise).
ABCD
was first shifted 3 units to the left and 5 units up, then rotated 90°
(counterclockwise).
upper A upper B upper C upper D was first shifted 3 units to the left and 5 units up, then rotated 90 degrees (counterclockwise).
ABCD
was first rotated −270°
(270°
clockwise), then shifted 3 units to the left and 5 units up.
Answers
Answered by
GPT-4o mini
To determine the two rigid transformations performed on quadrilateral ABCD to produce the congruent figure WXYZ, we can analyze the coordinates of both figures.
1. **Coordinates of Quadrilateral ABCD:**
- A (-6, -3)
- B (-6, -5)
- C (-4, -6)
- D (-3, -2)
2. **Coordinates of Quadrilateral WXYZ:**
- W (2, 9)
- X (0, 9)
- Y (-1, 7)
- Z (3, 6)
Now, we will calculate the transformations:
### Step 1: Shifting
- From point A (-6, -3) to point W (2, 9):
- The change in x-coordinates: 2 - (-6) = 2 + 6 = 8
- The change in y-coordinates: 9 - (-3) = 9 + 3 = 12
- This indicates a shift right (8 units) and up (12 units).
### Step 2: Rotation
After shifting the points, we need to analyze if a rotation transforms the new coordinates of ABCD into the coordinates of WXYZ.
If we calculate how much we need to rotate to match the transformation, we find that rotating -90° (or 90° clockwise) could match the respective new positions.
Thus, we can conclude that the transformations are as follows:
- **First transformation:** Shifted right 8 units and up 12 units (this matches with WXYZ).
- **Second transformation:** A further rotation of -90° (90° clockwise) makes the points align correctly.
From the transformation options provided:
**ABCD was first shifted 3 units to the left and 5 units up, then rotated -90° (90° clockwise).**
This is clearly not matching since we have already established it was shifted right? Hence, the transformations must thus align with the option given that it involved analysis derived earlier:
- ABCD was first rotated 90° (counterclockwise), then shifted parts accordingly.
### Correct response:
**ABCD was first rotated 90° (counterclockwise), then shifted 3 units to the left and 5 units up.**
1. **Coordinates of Quadrilateral ABCD:**
- A (-6, -3)
- B (-6, -5)
- C (-4, -6)
- D (-3, -2)
2. **Coordinates of Quadrilateral WXYZ:**
- W (2, 9)
- X (0, 9)
- Y (-1, 7)
- Z (3, 6)
Now, we will calculate the transformations:
### Step 1: Shifting
- From point A (-6, -3) to point W (2, 9):
- The change in x-coordinates: 2 - (-6) = 2 + 6 = 8
- The change in y-coordinates: 9 - (-3) = 9 + 3 = 12
- This indicates a shift right (8 units) and up (12 units).
### Step 2: Rotation
After shifting the points, we need to analyze if a rotation transforms the new coordinates of ABCD into the coordinates of WXYZ.
If we calculate how much we need to rotate to match the transformation, we find that rotating -90° (or 90° clockwise) could match the respective new positions.
Thus, we can conclude that the transformations are as follows:
- **First transformation:** Shifted right 8 units and up 12 units (this matches with WXYZ).
- **Second transformation:** A further rotation of -90° (90° clockwise) makes the points align correctly.
From the transformation options provided:
**ABCD was first shifted 3 units to the left and 5 units up, then rotated -90° (90° clockwise).**
This is clearly not matching since we have already established it was shifted right? Hence, the transformations must thus align with the option given that it involved analysis derived earlier:
- ABCD was first rotated 90° (counterclockwise), then shifted parts accordingly.
### Correct response:
**ABCD was first rotated 90° (counterclockwise), then shifted 3 units to the left and 5 units up.**