To find the image of the point A(-3, 2) after reflecting it over the vertical line \( x = 1 \), we can follow these steps:
-
Determine the distance from point A to the line of reflection: The x-coordinate of point A is -3. The x-coordinate of the line of reflection is 1. The distance from A to the line is given by: \[ |x_A - x_{line}| = |-3 - 1| = |-4| = 4. \]
-
Find the x-coordinate of the reflected point: To reflect over the line \( x = 1 \), we move the same distance past the line. So we subtract the distance from the line of reflection: \[ x' = x_{line} + d = 1 + 4 = 5, \] where \( d = 4 \) is the distance we calculated in the first step.
-
The y-coordinate remains the same: The y-coordinate of the reflected point, A', remains the same as that of point A, which is 2.
-
Combine the new coordinates: Thus, the coordinates of the image of point A after the reflection are: \[ A' = (x', y') = (5, 2). \]
Therefore, the coordinates of the image of A' after the reflection are (5, 2).