Question
Triangle PQR
is reflected over a vertical line of reflection to create triangle P′Q′R′
. What are the coordinates of point R′ (coordinate of R is (-11,1).
?
(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)
is reflected over a vertical line of reflection to create triangle P′Q′R′
. What are the coordinates of point R′ (coordinate of R is (-11,1).
?
(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
Answered by
GPT-4o mini
To find the coordinates of point \( R' \) after reflecting point \( R(-11, 1) \) over a vertical line of reflection, we need to know the x-coordinate of the line of reflection. However, since the vertical line of reflection is not specified in the question, we can only demonstrate the process for reflection.
For any vertical line of reflection at \( x = k \), the reflection of a point \( (x, y) \) can be calculated as follows:
1. The distance from the point to the line is given by \( d = x - k \).
2. The reflected point will be found by moving the same distance \( d \) to the opposite side of the line:
\[
x' = k - d
\]
So
\[
x' = k - (x - k) = 2k - x
\]
3. The y-coordinate remains unchanged.
Thus, if \( R = (-11, 1) \), the new coordinates depend on the vertical line of reflection. Without that information, \( R' \) can’t be definitely determined among the options you provided.
However, if we consider the options you provided, let’s evaluate them:
1. \( (1, -3) \)
2. \( (11, 1) \)
3. \( (-2, 7) \)
4. \( (-3, 1) \)
None of these options can be confirmed as correct without knowing the line of reflection.
If, for instance, we choose a line of reflection at \( x = 0 \) (the y-axis), the reflection of \( R \) would be:
\[
x' = 2(0) - (-11) = 11,
\]
and the y-coordinate remains 1.
Therefore, assuming a vertical reflection across the y-axis, the coordinates of \( R' \) would be \( (11, 1) \).
If the line of reflection was different, the coordinates could vary accordingly. Based on the most common scenarios, the best answer from the provided options, with a reflection across the y-axis, would be:
**(11, 1)**.
For any vertical line of reflection at \( x = k \), the reflection of a point \( (x, y) \) can be calculated as follows:
1. The distance from the point to the line is given by \( d = x - k \).
2. The reflected point will be found by moving the same distance \( d \) to the opposite side of the line:
\[
x' = k - d
\]
So
\[
x' = k - (x - k) = 2k - x
\]
3. The y-coordinate remains unchanged.
Thus, if \( R = (-11, 1) \), the new coordinates depend on the vertical line of reflection. Without that information, \( R' \) can’t be definitely determined among the options you provided.
However, if we consider the options you provided, let’s evaluate them:
1. \( (1, -3) \)
2. \( (11, 1) \)
3. \( (-2, 7) \)
4. \( (-3, 1) \)
None of these options can be confirmed as correct without knowing the line of reflection.
If, for instance, we choose a line of reflection at \( x = 0 \) (the y-axis), the reflection of \( R \) would be:
\[
x' = 2(0) - (-11) = 11,
\]
and the y-coordinate remains 1.
Therefore, assuming a vertical reflection across the y-axis, the coordinates of \( R' \) would be \( (11, 1) \).
If the line of reflection was different, the coordinates could vary accordingly. Based on the most common scenarios, the best answer from the provided options, with a reflection across the y-axis, would be:
**(11, 1)**.