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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)

Sagot :

chibabykalu16

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).

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