To reflect point A(-3, 2) over the vertical line \( x = 1 \), we first need to determine the horizontal distance between point A and the line \( x = 1 \).
-
The x-coordinate of point A is -3.
-
The distance from point A to the line \( x = 1 \) is: \[ d = 1 - (-3) = 1 + 3 = 4 \]
-
Since we are reflecting over the line, we will move 4 units to the right of the line \( x = 1 \).
-
The x-coordinate of the reflected point \( A' \) will then be: \[ x' = 1 + 4 = 5 \]
-
The y-coordinate remains the same during reflection, so the y-coordinate of \( A' \) is 2.
Thus, the coordinates of the image \( A' \) after reflection are: \[ A' (5, 2) \]