Question

will this work for all reflections over any line? yes no (circle one). 6) reflect the quadrilateral over the line x = - 2. p(-4, 4), q(0, 6), r(3, -1), s(-1, 2) p(_, _) q(_, _) r(_, _) s(_, _)

Explanation:

Step1: Recall reflection formula for x - axis line

For a reflection over the vertical line $x = a$, the formula for reflecting a point $(x,y)$ is $(2a - x,y)$. Here $a=-2$.

Step2: Reflect point P

For $P(-4,4)$, using the formula $x'=2\times(-2)-(-4)=-4 + 4=0$, $y' = 4$. So $P'(0,4)$.

Step3: Reflect point Q

For $Q(0,6)$, $x'=2\times(-2)-0=-4$, $y' = 6$. So $Q'(-4,6)$.

Step4: Reflect point R

For $R(3,-1)$, $x'=2\times(-2)-3=-4 - 3=-7$, $y'=-1$. So $R'(-7,-1)$.

Step5: Reflect point S

For $S(-1,2)$, $x'=2\times(-2)-(-1)=-4 + 1=-3$, $y' = 2$. So $S'(-3,2)$.

Answer:

$P'(0,4)$
$Q'(-4,6)$
$R'(-7,-1)$
$S'(-3,2)$