To reflect a point across a vertical line, you need to find the distance from the point to the line and then move that distance to the opposite side of the line.
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Identify the original point and the line: The original point is A(-3, 2), and the vertical line is given by x = 1.
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Calculate the distance from point A to the line: The x-coordinate of point A is -3. The vertical line x = 1 is 1 - (-3) = 4 units to the right of point A.
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Determine the x-coordinate of the reflected point: Since the line is to the right of point A, we will move 4 units to the right of the line to find the x-coordinate of the reflected point (A'). The x-coordinate would be: \[ 1 + 4 = 5 \]
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The y-coordinate remains the same: Since we are reflecting over a vertical line, the y-coordinate does not change. Therefore, the y-coordinate remains 2.
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Final coordinates of the image A': Combining both coordinates, the coordinates of the image A' are: \[ A' (5, 2) \]
So, the coordinates of the image A' are \( (5, 2) \).
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