Question

1. translate rectangle abcd. a(1,-1) b(4,-1) c(4,-3) d(1,-3) (x,y)→(x - 2,y + 5) label your translation.

Explanation:

Step1: Translate point A

Given $A(1,-1)$, use the rule $(x,y)\to(x - 2,y + 5)$. Substitute $x = 1$ and $y=-1$: $x-2=1 - 2=-1$, $y + 5=-1+5 = 4$. So the new - point $A'$ is $(-1,4)$.

Step2: Translate point B

Given $B(4,-1)$, substitute $x = 4$ and $y=-1$ into the rule $(x,y)\to(x - 2,y + 5)$. Then $x-2=4 - 2 = 2$, $y + 5=-1+5=4$. So the new - point $B'$ is $(2,4)$.

Step3: Translate point C

Given $C(4,-3)$, substitute $x = 4$ and $y=-3$ into the rule $(x,y)\to(x - 2,y + 5)$. Then $x-2=4 - 2=2$, $y + 5=-3 + 5=2$. So the new - point $C'$ is $(2,2)$.

Step4: Translate point D

Given $D(1,-3)$, substitute $x = 1$ and $y=-3$ into the rule $(x,y)\to(x - 2,y + 5)$. Then $x-2=1 - 2=-1$, $y + 5=-3+5 = 2$. So the new - point $D'$ is $(-1,2)$.

Answer:

The new vertices of the translated rectangle are $A'(-1,4)$, $B'(2,4)$, $C'(2,2)$, $D'(-1,2)$.