Question

identifying a translation
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?
four coordinate plane graphs with rectangles and options below, omitted here as per ocr instruction

Explanation:

Step1: Apply translation rule to \(D(-1,3)\)

For a translation \(T_{-1,2}(x,y)=(x - 1,y+2)\), when \(x=-1,y = 3\), we have \(D'(-1-1,3 + 2)=D'(-2,5)\)

Step2: Apply translation rule to \(E(4,3)\)

When \(x = 4,y=3\), \(E'(4-1,3 + 2)=E'(3,5)\)

Step3: Apply translation rule to \(F(4,1)\)

When \(x = 4,y = 1\), \(F'(4-1,1+2)=F'(3,3)\)

Step4: Apply translation rule to \(G(-1,1)\)

When \(x=-1,y = 1\), \(G'(-1-1,1+2)=G'(-2,3)\)

Answer:

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