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 $D(-1,3)$, $x=-1,y = 3$. Then $D'=(-1-1,3 + 2)=(-2,5)$.

Step3: Translate point E

For $E(4,3)$, $x = 4,y=3$. Then $E'=(4-1,3 + 2)=(3,5)$.

Step4: Translate point F

For $F(4,1)$, $x = 4,y = 1$. Then $F'=(4-1,1 + 2)=(3,3)$.

Step5: Translate point G

For $G(-1,1)$, $x=-1,y = 1$. Then $G'=(-1-1,1 + 2)=(-2,3)$.

Answer:

The new - image has coordinates $D'(-2,5),E'(3,5),F'(3,3),G'(-2,3)$.