Question

a graphic designer wants to translate rectangle defg using (t_{-1,2}(x,y)). the pre - image has coordinates d(-1,3), e(4,3), f(4,1), and g(-1,1). what is the image of defg?

Explanation:

Step1: Recall translation rule

The translation $T_{- 1,2}(x,y)=(x - 1,y + 2)$.

Step2: Translate point D

For $D(-1,3)$, substitute $x=-1$ and $y = 3$ into the rule: $D'=(-1-1,3 + 2)=(-2,5)$.

Step3: Translate point E

For $E(4,3)$, substitute $x = 4$ and $y=3$ into the rule: $E'=(4-1,3 + 2)=(3,5)$.

Step4: Translate point F

For $F(4,1)$, substitute $x = 4$ and $y = 1$ into the rule: $F'=(4-1,1 + 2)=(3,3)$.

Step5: Translate point G

For $G(-1,1)$, substitute $x=-1$ and $y = 1$ into the rule: $G'=(-1-1,1 + 2)=(-2,3)$.

The rectangle with vertices $D'(-2,5),E'(3,5),F'(3,3),G'(-2,3)$ is the correct image. (You would need to visually identify the corresponding graph among the options based on these coordinates).

Answer:

The image of rectangle DEFG has vertices $D'(-2,5),E'(3,5),F'(3,3),G'(-2,3)$.