Question

Question

Use the image to answer the question.

Triangle upper X (1,-1), upper Y(4,3), upper Z(6,0) 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.

Find the coordinates of Z′ after a reflection across y=1 .

(1 point)
Responses

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

Z′(4,0)
upper Z prime left parenthesis 4 comma 0 right parenthesis
Skip to navigation

Answer 1

To find the coordinates of \( Z' \) after reflecting the point \( Z(6,0) \) across the line \( y = 1 \), we need to follow these steps:

1. Determine the vertical distance from point \( Z \) to the line \( y = 1 \):

   • The y-coordinate of point \( Z \) is \( 0 \).
   • The y-coordinate of the line \( y = 1 \) is \( 1 \).
   • The distance from \( Z \) to the line is \( 1 - 0 = 1 \).

2. Reflect \( Z \) over the line \( y = 1 \):

   • Since \( Z \) is below the line \( y = 1 \) by 1 unit, we move 1 unit above the line to get the reflected point.
   • The y-coordinate of \( Z' \) would thus be \( 1 + 1 = 2 \).

3. Keep the x-coordinate the same during reflection (as the reflection is vertical):

   • The x-coordinate for point \( Z \) is \( 6 \), so the x-coordinate for point \( Z' \) will also be \( 6 \).

Therefore, the coordinates of \( Z' \) after the reflection are \( (6, 2) \).

So the correct response is: Z′(6,2)