Question

write the coordinates of the vertices after a reflection over the line ( x = -3 ).

Explanation:

Step1: Identify original coordinates

Original vertices: $R(-1, -1)$, $S(-1, 1)$, $T(1, 1)$

Step2: Recall reflection formula for $x=a$

For a point $(x,y)$, reflection over $x=a$ is $(2a - x, y)$. Here $a=-3$.

Step3: Calculate $R'$

Substitute $x=-1,y=-1,a=-3$:
$2(-3)-(-1) = -6 + 1 = -5$, so $R'(-5, -1)$

Step4: Calculate $S'$

Substitute $x=-1,y=1,a=-3$:
$2(-3)-(-1) = -5$, so $S'(-5, 1)$

Step5: Calculate $T'$

Substitute $x=1,y=1,a=-3$:
$2(-3)-1 = -6 -1 = -7$, so $T'(-7, 1)$

Answer:

$R'(-5, -1)$
$S'(-5, 1)$
$T'(-7, 1)$