To reflect a point over a vertical line, you can follow these steps:
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Identify the line of reflection: In this case, the line is \( x = 1 \).
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Determine the distance from the point to the line of reflection: For point A(-3, 2), the distance to the line \( x = 1 \) is calculated as follows: \[ \text{Distance} = |x_A - x_{\text{line}}| = |-3 - 1| = |-4| = 4. \]
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Reflect the point: To find the reflected point A′, you will move 4 units to the right of the line \( x = 1 \): \[ x_{A'} = x_{\text{line}} + \text{Distance} = 1 + 4 = 5. \] The y-coordinate remains the same, so \( y_A = 2 \).
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Final coordinates of the reflected point: Therefore, the coordinates of the image \( A' \) are (5, 2).
Thus, the coordinates of the image of A′ after reflection are \( A' = (5, 2) \).
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