Question

1. rectangle defg with vertices d(-4, 5), 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)

Explanation:

Step1: Find new coordinates of D

Given $D(-4,5)$ and transformation $(x,y)\to(x + 4,y + 1)$. For $x=-4$ and $y = 5$, we have $x'=-4 + 4=0$ and $y'=5+1 = 4$.

Step2: Find new coordinates of E

Given $E(0,2)$, for $x = 0$ and $y=2$, $x'=0 + 4=4$ and $y'=2+1=3$.

Step3: Find new coordinates of F

Given $F(-2,-6)$, for $x=-2$ and $y=-6$, $x'=-2 + 4=2$ and $y'=-6 + 1=-5$.

Step4: Find new coordinates of G

Given $G(-6,-5)$, for $x=-6$ and $y=-5$, $x'=-6+4=-2$ and $y'=-5 + 1=-4$.

Answer:

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