Question
Which graph correctly identifies rectangle QRST
being translated 2 units left and 4 units down?(1 point)
Responses
A. A coordinate plane shows all four quadrants with both axes ranging from negative 4 to 4 in unit increments. Eight points are plotted and are joined to form two rectangles of equal size. The vertices of the first rectangle labeled upper R upper S upper T upper Q are as follows: upper R is at left parenthesis 0 comma 3 right parenthesis, upper S is at left parenthesis 1 comma 3 right parenthesis, upper T is at left parenthesis 1 comma 0 right parenthesis, and upper Q is at left parenthesis 0 comma 0 right parenthesis. The vertices of the second rectangle labeled upper R prime, upper S prime, upper T prime, upper Q prime are as follows: upper R prime is at left parenthesis 0 comma negative 1 right parenthesis, upper S prime is at left parenthesis 1 comma negative 1 right parenthesis, upper T prime is at left parenthesis 1 comma negative 4 right parenthesis, and upper Q prime is at left parenthesis 0 comma negative 4 right parenthesis. The four points are joined by dotted lines.
Image with alt text: A coordinate plane shows all four quadrants with both axes ranging from negative 4 to 4 in unit increments. Eight points are plotted and are joined to form two rectangles of equal size. The vertices of the first rectangle labeled upper R upper S upper T upper Q are as follows: upper R is at left parenthesis 0 comma 3 right parenthesis, upper S is at left parenthesis 1 comma 3 right parenthesis, upper T is at left parenthesis 1 comma 0 right parenthesis, and upper Q is at left parenthesis 0 comma 0 right parenthesis. The vertices of the second rectangle labeled upper R prime, upper S prime, upper T prime, upper Q prime are as follows: upper R prime is at left parenthesis 0 comma negative 1 right parenthesis, upper S prime is at left parenthesis 1 comma negative 1 right parenthesis, upper T prime is at left parenthesis 1 comma negative 4 right parenthesis, and upper Q prime is at left parenthesis 0 comma negative 4 right parenthesis. The four points are joined by dotted lines.
B. A coordinate plane shows all four quadrants with both axes ranging from negative 4 to 4 in unit increments. Eight points are plotted and are joined to form two rectangles of equal size. The vertices of the first rectangle labeled upper R upper S upper T upper Q are as follows: upper R is at left parenthesis 0 comma 3 right parenthesis, upper S is at left parenthesis 1 comma 3 right parenthesis, upper T is at left parenthesis 1 comma 0 right parenthesis, and upper Q is at left parenthesis 0 comma 0 right parenthesis. The four points are joined by solid lines. The vertices of the second rectangle labeled upper R prime, upper S prime, upper T prime, upper Q prime are as follows: upper R prime is at left parenthesis negative 2 comma negative 1 right parenthesis, upper S prime is at left parenthesis negative 1 comma negative 1 right parenthesis, upper T prime is at left parenthesis negative 1 comma negative 4 right parenthesis, and upper Q prime is at left parenthesis negative 2 comma negative 4 right parenthesis. The four points are joined by dotted lines.
Image with alt text: A coordinate plane shows all four quadrants with both axes ranging from negative 4 to 4 in unit increments. Eight points are plotted and are joined to form two rectangles of equal size. The vertices of the first rectangle labeled upper R upper S upper T upper Q are as follows: upper R is at left parenthesis 0 comma 3 right parenthesis, upper S is at left parenthesis 1 comma 3 right parenthesis, upper T is at left parenthesis 1 comma 0 right parenthesis, and upper Q is at left parenthesis 0 comma 0 right parenthesis. The four points are joined by solid lines. The vertices of the second rectangle labeled upper R prime, upper S prime, upper T prime, upper Q prime are as follows: upper R prime is at left parenthesis negative 2 comma negative 1 right parenthesis, upper S prime is at left parenthesis negative 1 comma negative 1 right parenthesis, upper T prime is at left parenthesis negative 1 comma negative 4 right parenthesis, and upper Q prime is at left parenthesis negative 2 comma negative 4 right parenthesis. The four points are joined by dotted lines.
C. A coordinate plane shows all four quadrants with both axes ranging from negative 4 to 4 in unit increments. Eight points are plotted and are joined to form two rectangles of equal size. The vertices of the first rectangle labeled upper R upper S upper T upper Q are as follows: upper R is at left parenthesis 0 comma 3 right parenthesis, upper S is at left parenthesis 1 comma 3 right parenthesis, upper T is at left parenthesis 1 comma 0 right parenthesis, and upper Q is at left parenthesis 0 comma 0 right parenthesis. The four points are joined by solid lines. The vertices of the second rectangle labeled upper R prime, upper S prime, upper T prime, upper Q prime are as follows: upper R prime is at left parenthesis negative 2 comma 3 right parenthesis, upper S prime is at left parenthesis negative 1 comma 3 right parenthesis, upper T prime is at left parenthesis negative 1 comma 0 right parenthesis, and upper Q prime is at left parenthesis negative 2 comma 0 right parenthesis. The four points are joined by dotted lines.
Image with alt text: A coordinate plane shows all four quadrants with both axes ranging from negative 4 to 4 in unit increments. Eight points are plotted and are joined to form two rectangles of equal size. The vertices of the first rectangle labeled upper R upper S upper T upper Q are as follows: upper R is at left parenthesis 0 comma 3 right parenthesis, upper S is at left parenthesis 1 comma 3 right parenthesis, upper T is at left parenthesis 1 comma 0 right parenthesis, and upper Q is at left parenthesis 0 comma 0 right parenthesis. The four points are joined by solid lines. The vertices of the second rectangle labeled upper R prime, upper S prime, upper T prime, upper Q prime are as follows: upper R prime is at left parenthesis negative 2 comma 3 right parenthesis, upper S prime is at left parenthesis negative 1 comma 3 right parenthesis, upper T prime is at left parenthesis negative 1 comma 0 right parenthesis, and upper Q prime is at left parenthesis negative 2 comma 0 right parenthesis. The four points are joined by dotted lines.
D. A coordinate plane shows all four quadrants with both axes ranging from negative 4 to 4 in unit increments. Seven points are plotted and are joined to form two rectangles of equal size. The vertices of the first rectangle labeled upper R upper S upper T upper Q are as follows: upper R is at left parenthesis 0 comma 3 right parenthesis, upper S is at left parenthesis 1 comma 3 right parenthesis, upper T is at left parenthesis 1 comma 0 right parenthesis, and upper Q is at left parenthesis 0 comma 0 right parenthesis. The four points are joined by solid lines. The vertices of the second rectangle labeled upper R prime, upper S prime, upper T prime, upper Q prime are as follows: upper R prime is at left parenthesis negative 1 comma 0 right parenthesis, upper S prime is at left parenthesis 0 comma 0 right parenthesis, upper T prime is at left parenthesis 0 comma negative 3 right parenthesis, and upper Q prime is at left parenthesis negative 1 comma negative 3 right parenthesis. The four points are joined by dotted lines. The two rectangles share the point of origin.
Image with alt text: A coordinate plane shows all four quadrants with both axes ranging from negative 4 to 4 in unit increments. Seven points are plotted and are joined to form two rectangles of equal size. The vertices of the first rectangle labeled upper R upper S upper T upper Q are as follows: upper R is at left parenthesis 0 comma 3 right parenthesis, upper S is at left parenthesis 1 comma 3 right parenthesis, upper T is at left parenthesis 1 comma 0 right parenthesis, and upper Q is at left parenthesis 0 comma 0 right parenthesis. The four points are joined by solid lines. The vertices of the second rectangle labeled upper R prime, upper S prime, upper T prime, upper Q prime are as follows: upper R prime is at left parenthesis negative 1 comma 0 right parenthesis, upper S prime is at left parenthesis 0 comma 0 right parenthesis, upper T prime is at left parenthesis 0 comma negative 3 right parenthesis, and upper Q prime is at left parenthesis negative 1 comma negative 3 right parenthesis. The four points are joined by dotted lines. The two rectangles share the point of origin.
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being translated 2 units left and 4 units down?(1 point)
Responses
A. A coordinate plane shows all four quadrants with both axes ranging from negative 4 to 4 in unit increments. Eight points are plotted and are joined to form two rectangles of equal size. The vertices of the first rectangle labeled upper R upper S upper T upper Q are as follows: upper R is at left parenthesis 0 comma 3 right parenthesis, upper S is at left parenthesis 1 comma 3 right parenthesis, upper T is at left parenthesis 1 comma 0 right parenthesis, and upper Q is at left parenthesis 0 comma 0 right parenthesis. The vertices of the second rectangle labeled upper R prime, upper S prime, upper T prime, upper Q prime are as follows: upper R prime is at left parenthesis 0 comma negative 1 right parenthesis, upper S prime is at left parenthesis 1 comma negative 1 right parenthesis, upper T prime is at left parenthesis 1 comma negative 4 right parenthesis, and upper Q prime is at left parenthesis 0 comma negative 4 right parenthesis. The four points are joined by dotted lines.
Image with alt text: A coordinate plane shows all four quadrants with both axes ranging from negative 4 to 4 in unit increments. Eight points are plotted and are joined to form two rectangles of equal size. The vertices of the first rectangle labeled upper R upper S upper T upper Q are as follows: upper R is at left parenthesis 0 comma 3 right parenthesis, upper S is at left parenthesis 1 comma 3 right parenthesis, upper T is at left parenthesis 1 comma 0 right parenthesis, and upper Q is at left parenthesis 0 comma 0 right parenthesis. The vertices of the second rectangle labeled upper R prime, upper S prime, upper T prime, upper Q prime are as follows: upper R prime is at left parenthesis 0 comma negative 1 right parenthesis, upper S prime is at left parenthesis 1 comma negative 1 right parenthesis, upper T prime is at left parenthesis 1 comma negative 4 right parenthesis, and upper Q prime is at left parenthesis 0 comma negative 4 right parenthesis. The four points are joined by dotted lines.
B. A coordinate plane shows all four quadrants with both axes ranging from negative 4 to 4 in unit increments. Eight points are plotted and are joined to form two rectangles of equal size. The vertices of the first rectangle labeled upper R upper S upper T upper Q are as follows: upper R is at left parenthesis 0 comma 3 right parenthesis, upper S is at left parenthesis 1 comma 3 right parenthesis, upper T is at left parenthesis 1 comma 0 right parenthesis, and upper Q is at left parenthesis 0 comma 0 right parenthesis. The four points are joined by solid lines. The vertices of the second rectangle labeled upper R prime, upper S prime, upper T prime, upper Q prime are as follows: upper R prime is at left parenthesis negative 2 comma negative 1 right parenthesis, upper S prime is at left parenthesis negative 1 comma negative 1 right parenthesis, upper T prime is at left parenthesis negative 1 comma negative 4 right parenthesis, and upper Q prime is at left parenthesis negative 2 comma negative 4 right parenthesis. The four points are joined by dotted lines.
Image with alt text: A coordinate plane shows all four quadrants with both axes ranging from negative 4 to 4 in unit increments. Eight points are plotted and are joined to form two rectangles of equal size. The vertices of the first rectangle labeled upper R upper S upper T upper Q are as follows: upper R is at left parenthesis 0 comma 3 right parenthesis, upper S is at left parenthesis 1 comma 3 right parenthesis, upper T is at left parenthesis 1 comma 0 right parenthesis, and upper Q is at left parenthesis 0 comma 0 right parenthesis. The four points are joined by solid lines. The vertices of the second rectangle labeled upper R prime, upper S prime, upper T prime, upper Q prime are as follows: upper R prime is at left parenthesis negative 2 comma negative 1 right parenthesis, upper S prime is at left parenthesis negative 1 comma negative 1 right parenthesis, upper T prime is at left parenthesis negative 1 comma negative 4 right parenthesis, and upper Q prime is at left parenthesis negative 2 comma negative 4 right parenthesis. The four points are joined by dotted lines.
C. A coordinate plane shows all four quadrants with both axes ranging from negative 4 to 4 in unit increments. Eight points are plotted and are joined to form two rectangles of equal size. The vertices of the first rectangle labeled upper R upper S upper T upper Q are as follows: upper R is at left parenthesis 0 comma 3 right parenthesis, upper S is at left parenthesis 1 comma 3 right parenthesis, upper T is at left parenthesis 1 comma 0 right parenthesis, and upper Q is at left parenthesis 0 comma 0 right parenthesis. The four points are joined by solid lines. The vertices of the second rectangle labeled upper R prime, upper S prime, upper T prime, upper Q prime are as follows: upper R prime is at left parenthesis negative 2 comma 3 right parenthesis, upper S prime is at left parenthesis negative 1 comma 3 right parenthesis, upper T prime is at left parenthesis negative 1 comma 0 right parenthesis, and upper Q prime is at left parenthesis negative 2 comma 0 right parenthesis. The four points are joined by dotted lines.
Image with alt text: A coordinate plane shows all four quadrants with both axes ranging from negative 4 to 4 in unit increments. Eight points are plotted and are joined to form two rectangles of equal size. The vertices of the first rectangle labeled upper R upper S upper T upper Q are as follows: upper R is at left parenthesis 0 comma 3 right parenthesis, upper S is at left parenthesis 1 comma 3 right parenthesis, upper T is at left parenthesis 1 comma 0 right parenthesis, and upper Q is at left parenthesis 0 comma 0 right parenthesis. The four points are joined by solid lines. The vertices of the second rectangle labeled upper R prime, upper S prime, upper T prime, upper Q prime are as follows: upper R prime is at left parenthesis negative 2 comma 3 right parenthesis, upper S prime is at left parenthesis negative 1 comma 3 right parenthesis, upper T prime is at left parenthesis negative 1 comma 0 right parenthesis, and upper Q prime is at left parenthesis negative 2 comma 0 right parenthesis. The four points are joined by dotted lines.
D. A coordinate plane shows all four quadrants with both axes ranging from negative 4 to 4 in unit increments. Seven points are plotted and are joined to form two rectangles of equal size. The vertices of the first rectangle labeled upper R upper S upper T upper Q are as follows: upper R is at left parenthesis 0 comma 3 right parenthesis, upper S is at left parenthesis 1 comma 3 right parenthesis, upper T is at left parenthesis 1 comma 0 right parenthesis, and upper Q is at left parenthesis 0 comma 0 right parenthesis. The four points are joined by solid lines. The vertices of the second rectangle labeled upper R prime, upper S prime, upper T prime, upper Q prime are as follows: upper R prime is at left parenthesis negative 1 comma 0 right parenthesis, upper S prime is at left parenthesis 0 comma 0 right parenthesis, upper T prime is at left parenthesis 0 comma negative 3 right parenthesis, and upper Q prime is at left parenthesis negative 1 comma negative 3 right parenthesis. The four points are joined by dotted lines. The two rectangles share the point of origin.
Image with alt text: A coordinate plane shows all four quadrants with both axes ranging from negative 4 to 4 in unit increments. Seven points are plotted and are joined to form two rectangles of equal size. The vertices of the first rectangle labeled upper R upper S upper T upper Q are as follows: upper R is at left parenthesis 0 comma 3 right parenthesis, upper S is at left parenthesis 1 comma 3 right parenthesis, upper T is at left parenthesis 1 comma 0 right parenthesis, and upper Q is at left parenthesis 0 comma 0 right parenthesis. The four points are joined by solid lines. The vertices of the second rectangle labeled upper R prime, upper S prime, upper T prime, upper Q prime are as follows: upper R prime is at left parenthesis negative 1 comma 0 right parenthesis, upper S prime is at left parenthesis 0 comma 0 right parenthesis, upper T prime is at left parenthesis 0 comma negative 3 right parenthesis, and upper Q prime is at left parenthesis negative 1 comma negative 3 right parenthesis. The four points are joined by dotted lines. The two rectangles share the point of origin.
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Answers
GPT-4o mini
To determine which graph correctly represents the translation of rectangle QRST 2 units left and 4 units down, we start by identifying the original coordinates of rectangle QRST:
- R (0, 3)
- S (1, 3)
- T (1, 0)
- Q (0, 0)
### Translation Process
1. **Translate 2 units left:**
- R: (0 - 2, 3) = (-2, 3)
- S: (1 - 2, 3) = (-1, 3)
- T: (1 - 2, 0) = (-1, 0)
- Q: (0 - 2, 0) = (-2, 0)
2. **Translate 4 units down:**
- R: (-2, 3 - 4) = (-2, -1)
- S: (-1, 3 - 4) = (-1, -1)
- T: (-1, 0 - 4) = (-1, -4)
- Q: (-2, 0 - 4) = (-2, -4)
Thus, the new vertices after the translation will be:
- R' = (-2, -1)
- S' = (-1, -1)
- T' = (-1, -4)
- Q' = (-2, -4)
### Identifying the Correct Graph
Now, we will analyze the given options:
- **A:** R' = (0, -1), S' = (1, -1), T' = (1, -4), Q' = (0, -4) – **Inaccurate.**
- **B:** R' = (-2, -1), S' = (-1, -1), T' = (-1, -4), Q' = (-2, -4) – **Correct!**
- **C:** R' = (-2, 3), S' = (-1, 3), T' = (-1, 0), Q' = (-2, 0) – **Inaccurate.**
- **D:** R' = (-1, 0), S' = (0, 0), T' = (0, -3), Q' = (-1, -3) – **Inaccurate.**
### Conclusion
The correct answer is **B**, as it accurately represents the translation of rectangle QRST by moving it 2 units left and 4 units down.
- R (0, 3)
- S (1, 3)
- T (1, 0)
- Q (0, 0)
### Translation Process
1. **Translate 2 units left:**
- R: (0 - 2, 3) = (-2, 3)
- S: (1 - 2, 3) = (-1, 3)
- T: (1 - 2, 0) = (-1, 0)
- Q: (0 - 2, 0) = (-2, 0)
2. **Translate 4 units down:**
- R: (-2, 3 - 4) = (-2, -1)
- S: (-1, 3 - 4) = (-1, -1)
- T: (-1, 0 - 4) = (-1, -4)
- Q: (-2, 0 - 4) = (-2, -4)
Thus, the new vertices after the translation will be:
- R' = (-2, -1)
- S' = (-1, -1)
- T' = (-1, -4)
- Q' = (-2, -4)
### Identifying the Correct Graph
Now, we will analyze the given options:
- **A:** R' = (0, -1), S' = (1, -1), T' = (1, -4), Q' = (0, -4) – **Inaccurate.**
- **B:** R' = (-2, -1), S' = (-1, -1), T' = (-1, -4), Q' = (-2, -4) – **Correct!**
- **C:** R' = (-2, 3), S' = (-1, 3), T' = (-1, 0), Q' = (-2, 0) – **Inaccurate.**
- **D:** R' = (-1, 0), S' = (0, 0), T' = (0, -3), Q' = (-1, -3) – **Inaccurate.**
### Conclusion
The correct answer is **B**, as it accurately represents the translation of rectangle QRST by moving it 2 units left and 4 units down.