Question

write the coordinates of the vertices after a reflection over the line x = - 8. p( , ) q( , ) r( , )

Explanation:

Step1: Recall reflection formula

For a point $(x,y)$ reflected over the vertical line $x = a$, the new $x$-coordinate is $2a - x$ and the $y$-coordinate remains the same. Here $a=-8$.

Step2: Assume coordinates of points

Let's assume $P(x_1,y_1)$, $Q(x_2,y_2)$ and $R(x_3,y_3)$. Suppose $P(-4,-8)$, $Q(-4,-3)$, $R(-9,-8)$.

Step3: Calculate new $x$-coordinates for $P$

$x_{P'}=2\times(-8)-(-4)=-16 + 4=-12$, $y_{P'}=-8$. So $P'(-12,-8)$.

Step4: Calculate new $x$-coordinates for $Q$

$x_{Q'}=2\times(-8)-(-4)=-16 + 4=-12$, $y_{Q'}=-3$. So $Q'(-12,-3)$.

Step5: Calculate new $x$-coordinates for $R$

$x_{R'}=2\times(-8)-(-9)=-16 + 9=-7$, $y_{R'}=-8$. So $R'(-7,-8)$.

Answer:

$P'(-12,-8)$
$Q'(-12,-3)$
$R'(-7,-8)$