Question

the image of trapezoid abcd has coordinates a(-2,-5), b(-1,-2), c(2,-2), and d(3,-5). it was translated by the rule t_{-1,-3}(x,y). which diagram shows the pre - image?

Explanation:

Step1: Determine the translation rule for the pre - image

The translation rule for the image is \(T_{-1,-3}(x,y)=(x - 1,y - 3)\). To find the pre - image, we use the inverse rule. If \((x',y')=(x - 1,y - 3)\), then \(x=x'+1\) and \(y=y'+3\).

Step2: Calculate the coordinates of the pre - image

For \(A'(-2,-5)\):
\(x=-2 + 1=-1\), \(y=-5+3=-2\), so \(A(-1,-2)\)
For \(B'(-1,-2)\):
\(x=-1 + 1=0\), \(y=-2 + 3=1\), so \(B(0,1)\)
For \(C'(2,-2)\):
\(x=2 + 1=3\), \(y=-2+3 = 1\), so \(C(3,1)\)
For \(D'(3,-5)\):
\(x=3 + 1=4\), \(y=-5+3=-2\), so \(D(4,-2)\)

Answer:

The first diagram (assuming the first diagram has vertices \(A(-1,-2)\), \(B(0,1)\), \(C(3,1)\), \(D(4,-2)\)) shows the pre - image.