Answer:
K'(-4, -2)
Step-by-step explanation:
To determine the image coordinates of [tex] K' [/tex] when the pre-image is reflected across the line [tex] y = -4 [/tex], we need to follow these steps:
1. Identify the y-coordinate of point [tex] K [/tex], which is [tex] -6 [/tex].
2. Calculate the distance from [tex] K [/tex] to the line [tex] y = -4 [/tex]:
[tex] \text{Distance} = -4 - (-6) = 2 [/tex]
3. Reflect [tex] K [/tex] across the line [tex] y = -4 [/tex] by moving the same distance on the other side of the line:
[tex] y' = -4 + 2 = -2[/tex]
The x-coordinate of [tex] K [/tex] remains the same because the reflection is only in the y-direction.
Therefore, the coordinates of K' are (-4, -2).