To reflect a point over a vertical line, we need to determine how far the original point is from the line and then place the reflected point at the same distance on the opposite side.
The vertical line we are reflecting across is \( x = 1 \).
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Find the distance from point A to the vertical line:
The x-coordinate of point A is -3.
The distance from point A to the line \( x = 1 \) is: \[ 1 - (-3) = 1 + 3 = 4 \]
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Determine the x-coordinate of the reflected point A':
Since we are reflecting over the line, the image point will be the same distance from the line but on the opposite side. To find the x-coordinate of \( A' \), we need to add the distance to the line from point A:
The new x-coordinate will be: \[ 1 + 4 = 5 \]
Therefore, the x-coordinate of point A' is 5.
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Keep the y-coordinate the same:
The y-coordinate remains unchanged during a vertical reflection, so the y-coordinate of A' is still 2.
Thus, the coordinates of the image \( A' \) are: \[ A' (5, 2) \]
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