Question

write the coordinates of the vertices after a reflection over the line $y = -6$.
$a$( , )
$b$( , )
$c$( , )

Explanation:

Step1: Identify original coordinates

Original vertices: $A(1, -2)$, $B(5, -2)$, $C(-1, -5)$

Step2: Reflection formula for $y=k$

For a point $(x,y)$, reflection over $y=k$ is $(x, 2k - y)$. Here $k=-6$, so formula: $(x, 2(-6)-y)=(x, -12 - y)$

Step3: Calculate $A'$

Substitute $A(1,-2)$ into formula:
$A'(1, -12 - (-2)) = (1, -10)$

Step4: Calculate $B'$

Substitute $B(5,-2)$ into formula:
$B'(5, -12 - (-2)) = (5, -10)$

Step5: Calculate $C'$

Substitute $C(-1,-5)$ into formula:
$C'(-1, -12 - (-5)) = (-1, -7)$

Answer:

$A'(1, -10)$
$B'(5, -10)$
$C'(-1, -7)$