Question

1. reflection across x = 1

w(3, -3), x(2, 0), y(3, 1), z(5, -1)

Explanation:

Step1: Recall reflection formula

For a point $(x,y)$ reflected across the line $x = a$, the new - x - coordinate is $x'=2a - x$ and the y - coordinate remains the same, i.e., $y'=y$. Here $a = 1$.

Step2: Find the reflection of point W

For point $W(3,-3)$, $x = 3$ and $y=-3$. Using the formula $x'=2a - x=2\times1 - 3=-1$ and $y'=-3$. So the reflected point $W'(-1,-3)$.

Step3: Find the reflection of point X

For point $X(2,0)$, $x = 2$ and $y = 0$. Using the formula $x'=2a - x=2\times1 - 2 = 0$ and $y'=0$. So the reflected point $X'(0,0)$.

Step4: Find the reflection of point Y

For point $Y(3,1)$, $x = 3$ and $y = 1$. Using the formula $x'=2a - x=2\times1 - 3=-1$ and $y'=1$. So the reflected point $Y'(-1,1)$.

Step5: Find the reflection of point Z

For point $Z(5,-1)$, $x = 5$ and $y=-1$. Using the formula $x'=2a - x=2\times1 - 5=-3$ and $y'=-1$. So the reflected point $Z'(-3,-1)$.

Answer:

$W'(-1,-3),X'(0,0),Y'(-1,1),Z'(-3,-1)$