Polygon ABCD is drawn with vertices A(−4, −4), B(−4, −6), C(−1, −6), D(−1, −4). Determine the image coordinates of D′ if the preimage is reflected across y = 4.

Question

D′(5, −4)
D′(−2, −8)
D′(−1, 12)
D′(−1, 8)

Answer 1

To find the image coordinates \( D' \) of the point \( D(-1, -4) \) when reflected across the line \( y = 4 \), we follow these steps:

1. Determine the distance from point D to the line y = 4.

   • The y-coordinate of point D is \( -4 \).
   • The line \( y = 4 \) has a constant y-coordinate of \( 4 \).
   • The distance from \( D \) to the line is \( 4 - (-4) = 8 \) units.

2. Reflect point D across the line y = 4.

   • To reflect \( D \), we move \( 8 \) units above the line \( y = 4 \).
   • Starting from the line \( y = 4 \) and moving \( 8 \) units up, we reach \( 4 + 8 = 12 \).

3. Determine the x-coordinate of D'.

   • The x-coordinate of \( D \) does not change during reflection across a horizontal line; so it remains \( -1 \).

Thus, the coordinates of the reflected point \( D' \) are: \[ D' = (-1, 12) \]

Out of the given options, the correct answer is: \[ \boxed{(-1, 12)} \]