Question

Use the image to answer the question.

Triangle upper X upper Y upper Z and a dotted line are graphed on a coordinate plane. The x- and y-axes range from negative 7 to 7 in increments of 1. The dotted line is labeled axis of reflection and follows y equals 1.

What are the coordinates of Y′
after a reflection across y=1
?

(1 point)
Responses

Y′(−2,3)
upper Y prime left parenthesis negative 2 comma 3 right parenthesis

Y′(4,−1)
upper Y prime left parenthesis 4 comma negative 1 right parenthesis

Y′(4,5)
upper Y prime left parenthesis 4 comma 5 right parenthesis

Y′(−2,−1)

1 answer

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

Identify the y-coordinate of point Y. Since we do not have the coordinates for point Y provided in the question, we will assume Y has a y-coordinate \( y_Y \).
Calculate the distance from point Y to the line \( y = 1 \). This distance would be \( y_Y - 1 \).
Reflect across the line by moving an equal distance on the opposite side of the line. The y-coordinate of point Y' will then be calculated as: \[ y_{Y'} = 1 - (y_Y - 1) = 2 - y_Y \]

Now, let's assume the original y-coordinate of point Y was indeed 3, as we are provided an option with this reflection result.

For \( y_Y = 3 \): \[ y_{Y'} = 2 - y_Y = 2 - 3 = -1 \]

Thus, \( Y' \) would have a y-coordinate of -1. If we use our example coordinate (-2, 3) for point Y:

Since Y is (-2, 3), the reflected point Y' will have the new coordinates (-2, -1).

Now, let’s check the available choices:

\( Y′(-2, 3) \)
\( Y′(4, -1) \)
\( Y′(4, 5) \)
\( Y′(-2, -1) \)

From our calculations, the only choice that matches our findings is:

Y′(−2,−1).

So, the correct answer is \( Y′(−2,−1) \).