To find the coordinates of point \( Z' \) after reflection across the line \( y = 1 \), we need to know the original coordinates of point \( Z \).
However, if we assume \( Z \) has some coordinates \( (x, y) \), the reflection across the line \( y = 1 \) will maintain the x-coordinate, while the y-coordinate will change. The formula for the reflection across the horizontal line is given by the following:
\[ y' = 2k - y \]
where \( k \) is the y-value of the line of reflection (in this case, \( k = 1 \)).
Therefore, the new y-coordinate after reflection would be:
\[ y' = 2(1) - y = 2 - y \]
Now, we need to analyze the given response options to see which one could work based on common reflection results.
Test Each Response
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For \( Z′(−4, 0) \): \[ y' = 2 - 0 = 2 \quad \text{(not a match)} \]
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For \( Z′(−4, 2) \): \[ y' = 2 - 2 = 0 \quad \text{(not a match)} \]
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For \( Z′(6, 2) \): \[ y' = 2 - 2 = 0 \quad \text{(not a match)} \]
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For \( Z′(4, 0) \): \[ y' = 2 - 0 = 2 \quad \text{(matches \( y′ = 2 \))} \]
So the only point that after reflection across \( y = 1 \) gives the correct new coordinates is:
Answer:
\( Z′(4, 2) \)
1 answer