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: Recall translation rule reverse

The translation rule $T_{- 1,-3}(x,y)=(x - 1,y - 3)$ is given. To find the pre - image, we use the reverse rule $T_{1,3}(x,y)=(x + 1,y+3)$.

Step2: Find pre - image of $A'$

For $A'(-2,-5)$, applying the reverse rule: $x=-2,y = - 5$, then the pre - image $A$ has coordinates $(-2 + 1,-5 + 3)=(-1,-2)$.

Step3: Find pre - image of $B'$

For $B'(-1,-2)$, applying the reverse rule: $x=-1,y=-2$, then the pre - image $B$ has coordinates $(-1 + 1,-2 + 3)=(0,1)$.

Step4: Find pre - image of $C'$

For $C'(2,-2)$, applying the reverse rule: $x = 2,y=-2$, then the pre - image $C$ has coordinates $(2 + 1,-2 + 3)=(3,1)$.

Step5: Find pre - image of $D'$

For $D'(3,-5)$, applying the reverse rule: $x = 3,y=-5$, then the pre - image $D$ has coordinates $(3 + 1,-5 + 3)=(4,-2)$.

Answer:

Based on the calculated pre - image coordinates $A(-1,-2),B(0,1),C(3,1),D(4,-2)$, you would need to match these with the given diagrams to select the correct one. Since the diagrams are not labeled with coordinates here, the process to find the pre - image coordinates is shown above. If you were to graph these points, you can identify the correct pre - image trapezoid among the options.