Question

write the coordinates of the vertices after a reflection over the line $x=3$
$t(\square, \square)$
$u(\square, \square)$
$v(\square, \square)$
$w(\square, \square)$

Explanation:

Step1: Identify original coordinates

Original vertices: $T(-2, -3)$, $U(-2, 2)$, $V(0, 6)$, $W(1, 1)$

Step2: Recall reflection over $x=3$ rule

For a point $(x,y)$, reflection over $x=h$ is $(2h-x, y)$. Here $h=3$, so formula: $(6-x, y)$

Step3: Calculate $T'$

Substitute $x=-2,y=-3$: $6-(-2)=8$, so $T'(8, -3)$

Step4: Calculate $U'$

Substitute $x=-2,y=2$: $6-(-2)=8$, so $U'(8, 2)$

Step5: Calculate $V'$

Substitute $x=0,y=6$: $6-0=6$, so $V'(6, 6)$

Step6: Calculate $W'$

Substitute $x=1,y=1$: $6-1=5$, so $W'(5, 1)$

Answer:

$T'(8, -3)$
$U'(8, 2)$
$V'(6, 6)$
$W'(5, 1)$