Question

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

(1 point)
Responses

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 negative 4 comma 0 right parenthesis

Z′(4,0)

Answer 1

To find the coordinates of point \( Z' \) after a reflection across the line \( y = 1 \), we need to understand how reflections work.

1. Identify the original point \( Z \). However, the coordinates of \( Z \) are not provided in your question.
2. Since we're reflecting across the line \( y = 1 \), the distance from the point to this line will determine the new position.

For example, if point \( Z \) has coordinates \( (x, y) \):
- The vertical distance from point \( Z \) to the line \( y = 1 \) is \( y - 1 \).
- After reflection, this distance will be the same, but on the opposite side of the line.
- Thus, the y-coordinate of \( Z' \) will be \( 1 - (y - 1) = 2 - y \).

If we look at the options provided:
1. **Z'(-4, 2)**: The y-coordinate is 2, which means it would not change after reflecting over \( y=1 \) (it lies above the line).
2. **Z'(6, 2)**: Similar to the first, the y-coordinate is also 2.
3. **Z'(-4, 0)**: The y-coordinate is 0, which is below the line.
4. **Z'(4, 0)**: The y-coordinate is also 0, below the line.

Using the reflection rule:
- If the original point \( Z \) was at \( (-4, 0) \) or \( (4, 0) \), reflecting it across \( y = 1 \) gives the new coordinates \( (-4, 2) \) or \( (4, 2) \), respectively.

Thus, without loss of generality and assuming \( Z \) was at \( (-4, 0) \) or \( (4, 0) \), the correct choice for \( Z' \) after reflection across \( y = 1 \) would be:

**Z'(-4, 2)**.