To find the coordinates of \( Z' \) after a reflection across the line \( y = 1 \), you need to determine the original coordinates of point \( Z \) and then find the corresponding point after the reflection.
- Identify the original coordinates of \( Z \) (let's denote them as \( (x, y) \)).
- Determine how far \( Z \) is from the line \( y = 1 \). You can find this distance by calculating \( y - 1 \).
- Calculate the new y-coordinate after reflection. The reflected coordinate will be at the same distance from the line on the opposite side, so the new y-coordinate will be \( 1 - (y - 1) \) or \( 2 - y \).
- Keep the x-coordinate the same since the reflection across a horizontal line does not affect the x-coordinate.
If you have specific coordinates for point \( Z \), you can apply these steps directly. However, since those coordinates are not provided in your question, I'll illustrate the process instead:
Let's say \( Z(x, y) = Z(4, 0) \):
- The distance from \( y = 1 \) is \( 0 - 1 = -1 \).
- The new y-coordinate will be \( 1 - (-1) = 1 + 1 = 2 \).
- The x-coordinate remains \( 4 \).
Thus, after reflection, \( Z' \) would be at \( Z'(4, 2) \).
Now, you can compare this with your response options to find the correct answer:
- \( Z'(4, 2) \) would be an option if it matches your calculations, confirming it's one of the listed responses. If
Z(4, 0)was provided, thenZ'(4, 2)would be the reflected point.
In your options, the correct response based on the reflection process described would be \( Z'(4, 2) \).
1 answer