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Reflections Quick Check 5 of 55 of 5 Items Question Use the image to answer the question. Find the coordinates of Z′ after a reflection across y=1 . (1 point) Responses Z′(4,0) upper Z prime left parenthesis 4 comma 0 right parenthesis Z′(−4,2) upper Z prime left parenthesis negative 4 comma 2 right parenthesis Z′(−4,0) upper Z prime left parenthesis negative 4 comma 0 right parenthesis Z′(6,2) upper Z prime left parenthesis 6 comma 2 right parenthesis Skip to navigation page 19 of 19
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GPT-4o mini
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.
1. **Identify the original coordinates of \( Z \)** (let's denote them as \( (x, y) \)).
2. **Determine how far \( Z \) is from the line \( y = 1 \)**. You can find this distance by calculating \( y - 1 \).
3. **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 \( 2 - y \).
4. **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 \( Z(x, y) = Z(4, 0) \):
1. The distance from \( y = 1 \) is \( 0 - 1 = -1 \).
2. The new y-coordinate will be \( 1 - (-1) = 1 + 1 = 2 \).
3. 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, then `Z'(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. **Identify the original coordinates of \( Z \)** (let's denote them as \( (x, y) \)).
2. **Determine how far \( Z \) is from the line \( y = 1 \)**. You can find this distance by calculating \( y - 1 \).
3. **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 \( 2 - y \).
4. **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 \( Z(x, y) = Z(4, 0) \):
1. The distance from \( y = 1 \) is \( 0 - 1 = -1 \).
2. The new y-coordinate will be \( 1 - (-1) = 1 + 1 = 2 \).
3. 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, then `Z'(4, 2)` would be the reflected point.
In your options, the correct response based on the reflection process described would be \( Z'(4, 2) \).
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