To find the coordinates of point I' after reflecting point I over the line \( x = 1 \), we follow these steps:
-
Let's denote the coordinates of point I as \( (x, y) \).
-
The reflection of a point \( (x, y) \) over the line \( x = 1 \) can be found using the following formula:
\[ x' = 2 \times \text{line_x} - x \] where \(\text{line_x}\) is the x-coordinate of the line of reflection. In this case, \(\text{line_x} = 1\).
-
The y-coordinate remains the same, so \( y' = y \).
Now, we need to evaluate the reflection for each of the given points to find point I's coordinates:
-
For point (-5, 2):
\[ x' = 2 \times 1 - (-5) = 2 + 5 = 7 \] So, I' = (7, 2).
-
For point (5, 0):
\[ x' = 2 \times 1 - 5 = 2 - 5 = -3 \] So, I' = (-3, 0).
-
For point (-3, 2):
\[ x' = 2 \times 1 - (-3) = 2 + 3 = 5 \] So, I' = (5, 2).
-
For point (-2, 5):
\[ x' = 2 \times 1 - (-2) = 2 + 2 = 4 \] So, I' = (4, 5).
Since none of the reflections provided give us a final point that matches those listed, it appears your point I wasn't specified. However, we calculate reflection for each and none reflected generate the points provided initially.
If you meant the original coordinates I are one of those listed, please specify which one so the exact reflection over x=1 can be reported back.