Question

1. find the coordinates of the image after a reflection over $x = 1$

Explanation:

Step1: Identify original coordinates

Original points: $A(2, -1)$, $S(3, 2)$, $T(4, -3)$, $J(3, -4)$

Step2: Use reflection formula for $x=1$

For a point $(x,y)$, reflection over $x=h$ is $(2h-x,y)$. Here $h=1$, so formula is $(2(1)-x,y)=(2-x,y)$.

Step3: Calculate image of $A$

$A'(2-2, -1)=(0, -1)$

Step4: Calculate image of $S$

$S'(2-3, 2)=(-1, 2)$

Step5: Calculate image of $T$

$T'(2-4, -3)=(-2, -3)$

Step6: Calculate image of $J$

$J'(2-3, -4)=(-1, -4)$

Answer:

$A'(0, -1)$, $S'(-1, 2)$, $T'(-2, -3)$, $J'(-1, -4)$