Polygon JKLM is drawn with vertices J(−4, −4), K(−4, −6), L(−1, −6), M (−1, −4). Determine the image coordinates of L′ if the preimage is reflected across y = −2.
L′(−3, 6)
L′(−1, 6)
L′(−1, 2)
L′(1, 2)
To find the image coordinates of L′ after reflecting across y = -2, we first need to find the image of point L (-1, -6).
The distance between the line y = -2 and the point L (-1, -6) is 4 units. Therefore, the image point L′ will also be 4 units away from the line y = -2 on the other side.
Since L (−1, −6) is below the line y = -2, the image point L′ will be above the line. Adding 4 units to the y-coordinate of L (-1) gives us:
-6 + 4 = -2
Therefore, the image of L (-1, -6) after reflecting across y = -2 is L′ (-1, -2).
Therefore, the correct answer is:
L′(-1, 2)