Question

what are the coordinates of the image after the reflection in the given line.
$y = - 3$
a(
)
b(
)
c(
)
d(
)

Explanation:

Step1: Recall reflection rule

For a reflection over the line $y = k$, the $x$-coordinate of a point $(x,y)$ remains the same, and the new $y$-coordinate is calculated as $y'=2k - y$. Here $k=-3$.

Step2: Find coordinates of A'

Point A has coordinates $(3,1)$. Using the formula $y'=2\times(-3)-1=-6 - 1=-7$. So A' is $(3, -7)$.

Step3: Find coordinates of B'

Point B has coordinates $(6,3)$. Then $y'=2\times(-3)-3=-6 - 3=-9$. So B' is $(6, -9)$.

Step4: Find coordinates of C'

Point C has coordinates $(2,5)$. So $y'=2\times(-3)-5=-6 - 5=-11$. So C' is $(2, -11)$.

Step5: Find coordinates of D'

Point D has coordinates $(1,1)$. Then $y'=2\times(-3)-1=-6 - 1=-7$. So D' is $(1, -7)$.

Answer:

A'(3, -7)
B'(6, -9)
C'(2, -11)
D'(1, -7)