To find the coordinates of Point Q after it is reflected across the line \( x = -2 \), we need to apply the reflection formula.
The line \( x = -2 \) is a vertical line where every point on the line has an x-coordinate of -2. To reflect a point across this line, we will follow these steps:
- Determine the horizontal distance between the original point and the line of reflection.
- Place the reflected point on the opposite side of the line at the same distance.
For point \( Q (-4, 3) \):
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The x-coordinate of point Q is -4.
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The x-coordinate of the line \( x = -2 \) is -2.
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The distance from point Q to the line is: \[ -4 - (-2) = -4 + 2 = -2 \] This means point Q is 2 units to the left of the line.
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To find the x-coordinate of the reflected point \( Q' \), we move 2 units to the right of the line \( x = -2 \): \[ -2 + 2 = 0 \]
So the x-coordinate of \( Q' \) is 0. The y-coordinate remains the same since the reflection is horizontal.
Thus, the coordinates of the reflected point \( Q' \) are: \[ Q' (0, 3) \]
Therefore, the final answer is: \[ Q' (0, 3) \]