To determine the coordinates of point \( Y' \) after a reflection across the line \( y = 1 \), we first need to understand how a reflection works with respect to a horizontal line.
For a point with coordinates \( (x, y) \), when reflecting across the line \( y = k \) (in this case \( k = 1 \)), the new y-coordinate \( y' \) can be found using the formula: \[ y' = k - (y - k) = 2k - y \] where \( k \) is the y-coordinate of the line we are reflecting across.
- Identify the original point \( Y(x, y) \) (though it isn't specified in your question, we'll denote it generally).
- Calculate the new y-coordinate after reflection using \( y' = 2(1) - y = 2 - y \).
- The x-coordinate remains unchanged.
Assuming we are reflecting an unknown point \( Y(x, y) \), we can compare our results against the provided responses.
Let's evaluate the responses:
- \( Y'(-2, -1) \) → y-coordinate: -1 → needs calculation: \( 2 - (-1) = 3 \) (not correct)
- \( Y'(-2, 3) \) → y-coordinate: 3 → needs calculation: \( 2 - 3 = -1 \) (not correct)
- \( Y'(4, -1) \) → y-coordinate: -1 → needs calculation: \( 2 - (-1) = 3 \) (not correct)
- \( Y'(4, 5) \) → y-coordinate: 5 → needs calculation: \( 2 - 5 = -3 \) (not correct)
To find the correct answer, I would need the original coordinates of point \( Y \) to check which response corresponds.
Could you please provide the coordinates of point \( Y \)? This will allow us to accurately find \( Y' \).
1 answer