Question

1. write the coordinates of the image given a reflection over $x = -3$

Explanation:

Step1: Identify original coordinates

Original points: $I(-5, 0)$, $P(-4, -2)$, $S(-2, 1)$, $W(-2, 4)$

Step2: Use reflection formula for $x=-3$

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

Step3: Calculate $I'$

Substitute $x=-5$: $-6-(-5) = -1$, $y=0$
$I' = (-1, 0)$

Step4: Calculate $P'$

Substitute $x=-4$: $-6-(-4) = -2$, $y=-2$
$P' = (-2, -2)$

Step5: Calculate $S'$

Substitute $x=-2$: $-6-(-2) = -4$, $y=1$
$S' = (-4, 1)$

Step6: Calculate $W'$

Substitute $x=-2$: $-6-(-2) = -4$, $y=4$
$W' = (-4, 4)$

Answer:

$I'(-1, 0)$, $P'(-2, -2)$, $S'(-4, 1)$, $W'(-4, 4)$