Question

1. parallelogram wxyz with vertices w(-3, -2), x(1, 0), y(0, -5), and z(-4, -7); translated along the rule (x, y) → (x + 6, y + 7)

w (_, _)
x (_, _)
y (_, _)
z (_, _)

Explanation:

Step1: Translate point W

Given $W(-3,-2)$ and the translation rule $(x,y)\to(x + 6,y + 7)$. For the x - coordinate of $W'$, we have $x=-3+6 = 3$. For the y - coordinate of $W'$, we have $y=-2 + 7=5$. So $W'(3,5)$.

Step2: Translate point X

Given $X(1,0)$ and the translation rule $(x,y)\to(x + 6,y + 7)$. For the x - coordinate of $X'$, we have $x=1+6 = 7$. For the y - coordinate of $X'$, we have $y=0 + 7=7$. So $X'(7,7)$.

Step3: Translate point Y

Given $Y(0,-5)$ and the translation rule $(x,y)\to(x + 6,y + 7)$. For the x - coordinate of $Y'$, we have $x=0+6 = 6$. For the y - coordinate of $Y'$, we have $y=-5 + 7=2$. So $Y'(6,2)$.

Step4: Translate point Z

Given $Z(-4,-7)$ and the translation rule $(x,y)\to(x + 6,y + 7)$. For the x - coordinate of $Z'$, we have $x=-4+6 = 2$. For the y - coordinate of $Z'$, we have $y=-7 + 7=0$. So $Z'(2,0)$.

Answer:

$W'(3,5)$
$X'(7,7)$
$Y'(6,2)$
$Z'(2,0)$