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 the translation rule in reverse

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

Step2: Find the pre - image coordinates of $A'$

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

Step3: Find the pre - image coordinates of $B'$

For $B'(-1,-2)$, $x=-1,y=-2$. Then the pre - image $B$ has coordinates $x=-1 + 1=0,y=-2 + 3=1$, so $B(0,1)$.

Step4: Find the pre - image coordinates of $C'$

For $C'(2,-2)$, $x = 2,y=-2$. Then the pre - image $C$ has coordinates $x=2 + 1=3,y=-2 + 3=1$, so $C(3,1)$.

Step5: Find the pre - image coordinates of $D'$

For $D'(3,-5)$, $x = 3,y=-5$. Then the pre - image $D$ has coordinates $x=3 + 1=4,y=-5 + 3=-2$, so $D(4,-2)$.
Then we can match the trapezoid with these pre - image coordinates among the given diagrams.

Answer:

(You need to visually check the diagrams with the calculated pre - image coordinates $A(-1,-2),B(0,1),C(3,1),D(4,-2)$ to determine the correct one. Since the diagrams are not labeled with coordinates here, the final visual selection is up to you based on the above - calculated points.)