To find the coordinates of point R' after Triangle PQR is reflected over a vertical line, we first need to determine the vertical line of reflection.
We know the coordinates of point R are (-11, 1) and point R' has yet to be determined. We also have the coordinates of point P and P' that can help us find the line of reflection.
Coordinates of point P: P(-8, 9) Coordinates of point P' after reflection: P'(-6, 9)
The reflection over a vertical line means that the y-coordinates remain the same, and the x-coordinates will be symmetrical about the line of reflection. To find this line, we can calculate the midpoint of points P and P'.
Midpoint of P and P': \[ \text{Midpoint} = \left( \frac{-8 + (-6)}{2}, \frac{9 + 9}{2} \right) = \left( \frac{-14}{2}, 9 \right) = (-7, 9) \]
The line of reflection must be x = -7.
To find R', we will use the same reflection rule: the distance from R to the line of reflection should equal the distance from R' to the line of reflection.
The coordinates of point R are (-11, 1). The distance from R to the line x = -7 is: \[ |-11 - (-7)| = |-11 + 7| = |-4| = 4 \]
Since we are reflecting R over the line x = -7, R' will be 4 units from the line on the opposite side.
To find R', we calculate the x-coordinate: \[ -7 + 4 = -3 \] The y-coordinate remains the same: \[ y' = y = 1 \]
Thus, the coordinates of R' are (-3, 1).
Therefore, the coordinates of point R' are: D. (-3, 1)