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 $x$ - coordinate is decreased by 1 and $y$ - coordinate is increased by 2.

Step2: Translate point D

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

Step3: Translate point E

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

Step4: Translate point F

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

Step5: Translate point G

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

Answer:

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