Polygon JKLM is drawn with vertices J(−4, −3), K(−4, −6), L(−1, −6), M(−1, −3). Determine the image coordinates of K′ if the pre-image is reflected across y = −4.
K′(−4, −4)
K′(4, −6)
K′(−4, 6)
K′(−4, −2)
To reflect the point K(-4, -6) across the line y = -4, we need to find the distance between K and the line y = -4 and then move that same distance on the other side of the line.
The distance between K and the line y = -4 is 2 units (from -6 to -4). Since we are reflecting across the line y = -4, we need to move 2 units in the opposite direction.
Therefore, the image coordinate of K' will be 2 units above the line y = -4, which is at y = -2. The x-coordinate will remain the same, which is -4.
So, the correct answer is K'(-4, -2).