Polygon JKLM is drawn with vertices J(−4, −4), K(−4, −6), L(−1, −6), M(−1, −4). Determine the image coordinates of K′ if the preimage is reflected across y = −7.

Question

K′(−4, −4)
K′(−4, −5)
K′(−4, 6)
K′(−4, −8)

Answer 1

To reflect the point \( K(-4, -6) \) across the line \( y = -7 \), we can follow these steps:

1. Determine the distance from the point to the line: The y-coordinate of point K is -6. The line \( y = -7 \) is below point K, so we find the distance between -6 and -7.

   \[ \text{Distance} = -6 - (-7) = -6 + 7 = 1 \]

2. Find the reflected point: Since the distance is 1 unit above the line, the reflected point will be 1 unit below the line \( y = -7 \).

   \[ y\text{-coordinate of } K' = -7 - 1 = -8 \]

3. Keep the x-coordinate the same: The x-coordinate of K is -4, therefore the coordinates of the reflected point \( K' \) are:

   \[ K'(-4, -8) \]

The image coordinates of \( K' \) are \( (-4, -8) \). Therefore, the correct choice among the options provided is:

K′(−4, −8).