Question

Find the coordinates of Z′ after a reflection across y=1.

(1 point)
Responses

Z′(−4,0)
upper Z prime left parenthesis negative 4 comma 0 right parenthesis

Z′(−4,2)
upper Z prime left parenthesis negative 4 comma 2 right parenthesis

Z′(6,2)
upper Z prime left parenthesis 6 comma 2 right parenthesis

Z′(4,0)
upper Z prime left parenthesis 4 comma 0 right parenthesis

Answer 1

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
1. **For \( Z′(−4, 0) \)**:
\[
y' = 2 - 0 = 2 \quad \text{(not a match)}
\]

2. **For \( Z′(−4, 2) \)**:
\[
y' = 2 - 2 = 0 \quad \text{(not a match)}
\]

3. **For \( Z′(6, 2) \)**:
\[
y' = 2 - 2 = 0 \quad \text{(not a match)}
\]

4. **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:
\( Z′(4, 2) \)