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 $T_{- 1,2}(x,y)$ means we subtract 1 from the $x$-coordinate and add 2 to the $y$-coordinate of each point.

Step2: Translate point D

For $D(-1,3)$, $x=-1,y = 3$. New $x=-1-1=-2$, new $y=3 + 2=5$. So $D'(-2,5)$.

Step3: Translate point E

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

Step4: Translate point F

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

Step5: Translate point G

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

Answer:

The coordinates of the image are $D'(-2,5),E'(3,5),F'(3,3),G'(-2,3)$