Use the image to answer the question.

To find the coordinates of \( Y' \) after reflecting point \( Y \) across the line \( y = 1 \), we can follow these steps:

1. Identify the original coordinates of point \( Y \). (Since the image is not provided, we assume a hypothetical point for explanation. Let’s say \( Y(x, y) \).)

2. Determine the distance from point \( Y \) to the line of reflection \( y = 1 \): \[ \text{Distance} = y - 1 \] (If \( y < 1 \), the distance will be negative because the point is below the line.)

3. Reflect the point:

   • If \( Y \) is above the line \( y = 1 \), then the reflected point \( Y' \) will be: \[ Y'(x, 1 - \text{Distance}) = Y'(x, 1 - (y - 1)) = Y'(x, 2 - y) \]
   • If \( Y \) is below the line \( y = 1 \), then the reflected point \( Y' \) will be: \[ Y'(x, 1 + |\text{Distance}|) = Y'(x, 1 + (1 - y)) = Y'(x, 2 - y) \]

In either case, the y-coordinate of the reflected point can be found using \( Y'(x, 2 - y) \).

Now, let's evaluate the options provided based on the reflection rule derived:

• Option 1: \( Y'(-2, -1) \)

• Option 2: \( Y'(4, 5) \)

• Option 3: \( Y'(-2, 3) \)

• Option 4: \( Y'(4, -1) \)

Since we need \( Y' \) such that its y-coordinate is \( 2 - y \) and should yield a point above the line \( y = 1 \times 2 \), we evaluate each option based on whether \( y \) of the original point \( Y \) makes sense.

• If \( y = 3 \), then \( Y' \) is \( (x, 2 - 3) = (x, -1) \) which leads to \( Y'(-2, -1) \).
• If \( y = 5 \), then \( Y' \) is \( (x, 2 - 5) = (x, -3) \).
• If \( y = -1 \), then \( Y' \) becomes \( (x, 2 + 1) = (x, 3) \).
• If \( y = -1 \), it leads to \( (x, 3) \), similar conclusion can be drawn.

Through geometrical reasoning based on the axis of reflection and given coordinate outcomes, the most reasonable coordinate after the reflected state around \( y = 1 \) is \( Y'(-2, 3) \).

So, the final answer should be:

Y′(−2, 3)