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

Step2: Translate point D

For point D(-1,3), applying the rule: $x=-1,y = 3$, then $x-1=-1 - 1=-2$ and $y + 2=3 + 2 = 5$. So D' is (-2,5).

Step3: Translate point E

For point E(4,3), $x = 4,y = 3$, then $x-1=4-1 = 3$ and $y + 2=3 + 2=5$. So E' is (3,5).

Step4: Translate point F

For point F(4,1), $x = 4,y = 1$, then $x-1=4-1=3$ and $y + 2=1 + 2 = 3$. So F' is (3,3).

Step5: Translate point G

For point G(-1,1), $x=-1,y = 1$, then $x-1=-1-1=-2$ and $y + 2=1 + 2=3$. So G' is (-2,3).

Answer:

The new - coordinates of the rectangle D'E'F'G' have vertices D'(-2,5), E'(3,5), F'(3,3), G'(-2,3). (Since no specific multiple - choice options are given, this is the general result of the translation).