Question

1. quadrilateral wxyz with vertices w(-1, 1), x(2, -3), y(0, -6), and z(-2, -5): x = -3 w(_, _) x(_, _) y(_, _) z(_, _)

Explanation:

Step1: Recall reflection formula

For a point $(x,y)$ reflected over the line $x = a$, the new - x - coordinate is $2a - x$ and the y - coordinate remains the same. Here $a=-3$.

Step2: Find coordinates of $W'$

For point $W(-1,1)$, the new x - coordinate is $2\times(-3)-(-1)=-6 + 1=-5$, and the y - coordinate is $1$. So $W'(-5,1)$.

Step3: Find coordinates of $X'$

For point $X(2,-3)$, the new x - coordinate is $2\times(-3)-2=-6 - 2=-8$, and the y - coordinate is $-3$. So $X'(-8,-3)$.

Step4: Find coordinates of $Y'$

For point $Y(0,-6)$, the new x - coordinate is $2\times(-3)-0=-6$, and the y - coordinate is $-6$. So $Y'(-6,-6)$.

Step5: Find coordinates of $Z'$

For point $Z(-2,-5)$, the new x - coordinate is $2\times(-3)-(-2)=-6 + 2=-4$, and the y - coordinate is $-5$. So $Z'(-4,-5)$.

Answer:

$W'(-5,1)$
$X'(-8,-3)$
$Y'(-6,-6)$
$Z'(-4,-5)$