Question
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A vertical line separates 2 triangles. The triangle to the left of the line is made up of points upper P, upper Q, and upper R, while the triangle on the right is made up of points upper P prime, upper Q prime, and upper R prime. Use the image to answer the question. Triangle PQR is reflected over a vertical line of reflection to create triangle P′Q′R′ . What are the coordinates of point R′ ? (1 point) Responses (1,−3) left parenthesis 1 comma negative 3 right parenthesis (11,1) left parenthesis 11 comma 1 right parenthesis (−2,7) left parenthesis negative 2 comma 7 right parenthesis (−3,1)
A vertical line separates 2 triangles. The triangle to the left of the line is made up of points upper P, upper Q, and upper R, while the triangle on the right is made up of points upper P prime, upper Q prime, and upper R prime. Use the image to answer the question. Triangle PQR is reflected over a vertical line of reflection to create triangle P′Q′R′ . What are the coordinates of point R′ ? (1 point) Responses (1,−3) left parenthesis 1 comma negative 3 right parenthesis (11,1) left parenthesis 11 comma 1 right parenthesis (−2,7) left parenthesis negative 2 comma 7 right parenthesis (−3,1)
Answers
Answer
Triangle PQR is reflected over a vertical line of reflection to create triangle P′Q′R′ . What are the coordinates of point R′ ? (1 point) Responses (1,−3) left parenthesis 1 comma negative 3 right parenthesis (11,1) left parenthesis 11 comma 1 right parenthesis (−2,7) left parenthesis negative 2 comma 7 right parenthesis (−3,1)
Answered by
GPT-4o mini
To find the coordinates of point \( R' \) after reflection, we need to know the coordinates of point \( R \) and the vertical line of reflection. Since the specific coordinates of point \( R \) and the line of reflection are not provided in your question, we will assume the vertical line is given by \( x = c \).
The reflection across a vertical line such as \( x = c \) means that the x-coordinate of any point gets transformed according to the formula:
\[
R' = (2c - x_R, y_R)
\]
where \( (x_R, y_R) \) are the coordinates of the original point \( R \).
1. If \( c \) is the x-coordinate of the line of reflection and you know \( R \)'s coordinates, plug in \( x_R \) and \( y_R \) into the formula above.
2. The resulting point \( R' \) should be in the form \( (x', y_R) \) where \( x' = 2c - x_R \).
Assuming you have point \( R \)'s coordinates and the reflection line, calculate \( R' \) accordingly.
If you can provide the coordinates of point \( R \) and the position of the vertical line, I can give you a specific answer for \( R' \). If not, please check the multiple-choice responses against your findings.
The reflection across a vertical line such as \( x = c \) means that the x-coordinate of any point gets transformed according to the formula:
\[
R' = (2c - x_R, y_R)
\]
where \( (x_R, y_R) \) are the coordinates of the original point \( R \).
1. If \( c \) is the x-coordinate of the line of reflection and you know \( R \)'s coordinates, plug in \( x_R \) and \( y_R \) into the formula above.
2. The resulting point \( R' \) should be in the form \( (x', y_R) \) where \( x' = 2c - x_R \).
Assuming you have point \( R \)'s coordinates and the reflection line, calculate \( R' \) accordingly.
If you can provide the coordinates of point \( R \) and the position of the vertical line, I can give you a specific answer for \( R' \). If not, please check the multiple-choice responses against your findings.
Answered by
GPT-4o mini
To determine the coordinates of point \( R' \) after triangle \( PQR \) is reflected over a vertical line, we need to know the coordinates of point \( R \) and the vertical line of reflection. Since this information wasn't provided, I'll clarify how to find \( R' \) based on the general rules of reflection over a vertical line.
When reflecting over a vertical line, the x-coordinate changes according to the distance from the vertical line to the original point, but the y-coordinate remains the same. For a vertical line of reflection at \( x = k \):
1. If the coordinates of point \( R \) are \( (x_R, y_R) \), then the reflection would be calculated as follows:
\[
R' = (2k - x_R, y_R)
\]
The challenge here is that we don't know the specific values for \( x_R \) or \( k \).
### Assuming potential coordinates for R
Let's hypothesize the following:
- If \( R \) has coordinates \( (x_R, y_R) = (0, 1) \) and it reflects over the line \( x = 5 \):
- The new x-coordinate \( R' \) would be:
\[
x' = 2 \cdot 5 - 0 = 10
\]
- The y-coordinate remains the same:
\[
y' = y_R = 1 \implies R' = (10, 1)
\]
### Using the given multiple-choice responses
Without specific coordinates for point \( R \) and the line of reflection, we cannot determine the exact position of \( R' \). However, we can analyze the responses:
- **(1, -3)**
- **(11, 1)**
- **(-2, 7)**
- **(-3, 1)**
If you have more context (e.g., the coordinates of the original triangle or the line of reflection), I would be able to give you a precise answer. However, based on the multiple choices, the formatted pairs could match those of the new coordinates based on your determination of the reflection.
Please provide the coordinates of point \( R \) and the position of the vertical line if available, or just select the answer that seems reasonable based on your triangle's reflection.
When reflecting over a vertical line, the x-coordinate changes according to the distance from the vertical line to the original point, but the y-coordinate remains the same. For a vertical line of reflection at \( x = k \):
1. If the coordinates of point \( R \) are \( (x_R, y_R) \), then the reflection would be calculated as follows:
\[
R' = (2k - x_R, y_R)
\]
The challenge here is that we don't know the specific values for \( x_R \) or \( k \).
### Assuming potential coordinates for R
Let's hypothesize the following:
- If \( R \) has coordinates \( (x_R, y_R) = (0, 1) \) and it reflects over the line \( x = 5 \):
- The new x-coordinate \( R' \) would be:
\[
x' = 2 \cdot 5 - 0 = 10
\]
- The y-coordinate remains the same:
\[
y' = y_R = 1 \implies R' = (10, 1)
\]
### Using the given multiple-choice responses
Without specific coordinates for point \( R \) and the line of reflection, we cannot determine the exact position of \( R' \). However, we can analyze the responses:
- **(1, -3)**
- **(11, 1)**
- **(-2, 7)**
- **(-3, 1)**
If you have more context (e.g., the coordinates of the original triangle or the line of reflection), I would be able to give you a precise answer. However, based on the multiple choices, the formatted pairs could match those of the new coordinates based on your determination of the reflection.
Please provide the coordinates of point \( R \) and the position of the vertical line if available, or just select the answer that seems reasonable based on your triangle's reflection.
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