To find the coordinates of point Q after it is reflected across the line \( x = -2 \), follow these steps:
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Identify the original coordinates of point Q: Let's denote the coordinates of point Q as \( (x_Q, y_Q) \).
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Determine the distance from the point to the line: The line \( x = -2 \) is a vertical line. The distance from point Q to this line can be determined as follows: \[ \text{Distance} = x_Q - (-2) = x_Q + 2 \]
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Find the reflected x-coordinate: The reflected point will be the same distance on the opposite side of the line. Therefore, we can calculate the new x-coordinate \( x_Q' \) as follows: \[ x_Q' = -2 - (x_Q + 2) = -2 - x_Q - 2 = -x_Q - 4 \]
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Retain the y-coordinate: The y-coordinate remains the same after reflection across a vertical line. Thus, the new y-coordinate \( y_Q' \) will simply be \( y_Q \).
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Final coordinates of the reflected point: Putting this all together, the coordinates of point Q after reflection across the line \( x = -2 \) will be: \[ Q' = (-x_Q - 4, y_Q) \]
If you provide the specific coordinates of point Q, I can give you the exact coordinates of the reflected point Q'.
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