Question

rectangle defg with vertices d(-4, 3), e(0, 2), f(-2, -6), and g(-6, -5); (x, y)→(x + 4, y + 1)
d(0, 4)
e(4, 3)
f(2, -5)
g(-2, -4)
rule: (x, x)→(x, x - 7)

Explanation:

Step1: Apply rule to point D

For point $D(-4,3)$, using the rule $(x,y)\to(x + 4,y + 1)$, we have $x=-4$ and $y = 3$. Then $x+4=-4 + 4=0$ and $y + 1=3+1 = 4$. So $D'=(0,4)$.

Step2: Apply rule to point E

For point $E(0,2)$, with $x = 0$ and $y=2$, $x + 4=0+4=4$ and $y + 1=2 + 1=3$. So $E'=(4,3)$.

Step3: Apply rule to point F

For point $F(-2,-6)$, where $x=-2$ and $y=-6$, $x + 4=-2+4=2$ and $y + 1=-6 + 1=-5$. So $F'=(2,-5)$.

Step4: Apply rule to point G

For point $G(-6,-5)$, with $x=-6$ and $y=-5$, $x + 4=-6+4=-2$ and $y + 1=-5 + 1=-4$. So $G'=(-2,-4)$.

Answer:

$D'(0,4),E'(4,3),F'(2,-5),G'(-2,-4)$