To find the coordinates of point \( R' \) after triangle \( PQR \) is reflected over a vertical line, we need to know the equation of the vertical line of reflection.
A vertical line will take the form \( x = k \), where \( k \) is a constant representing the x-coordinate of the line.
When a point \( (x, y) \) is reflected over a vertical line \( x = k \), the x-coordinate of the reflected point \( (x', y) \) is given by the formula:
\[ x' = 2k - x \]
The y-coordinate remains the same.
Given that the coordinates of point \( R \) are \( R = (-11, 1) \), we can find the coordinates of point \( R' \) once we know the line \( x = k \).
If we assume the line of reflection is \( x = k \), we can plug in the values. For instance, if the line of reflection were \( x = 0 \):
- The x-coordinate of \( R \) is \( -11 \).
- Reflecting over \( x = 0 \):
\[ x' = 2(0) - (-11) = 11 \]
- The y-coordinate remains the same, so:
\[ y' = 1 \]
Thus, the coordinates of point \( R' \) would be \( R' = (11, 1) \).
You would replace \( k \) with the actual line of reflection if it's different. If you provide the specific vertical line of reflection, I can calculate the exact coordinates for \( R' \).
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