graph the image of rectangle defg after a translation 3 units right and 3 units up.

Explanation:

Step1: Recall translation rule

For a point $(x,y)$ translated 3 units right and 3 units up, the new - point is $(x + 3,y+3)$.

Step2: Find coordinates of vertices of original rectangle

From the graph, the coordinates of the vertices of rectangle $DEFG$ are: $D(-6,-8)$, $E(2,-8)$, $F(2,2)$, $G(-6,2)$.

Step3: Apply translation rule to point D

For point $D(-6,-8)$, the new $x$ - coordinate is $x=-6 + 3=-3$, and the new $y$ - coordinate is $y=-8 + 3=-5$. So the new point $D'$ is $(-3,-5)$.

Step4: Apply translation rule to point E

For point $E(2,-8)$, the new $x$ - coordinate is $x=2 + 3=5$, and the new $y$ - coordinate is $y=-8 + 3=-5$. So the new point $E'$ is $(5,-5)$.

Step5: Apply translation rule to point F

For point $F(2,2)$, the new $x$ - coordinate is $x=2+3 = 5$, and the new $y$ - coordinate is $y=2 + 3=5$. So the new point $F'$ is $(5,5)$.

Step6: Apply translation rule to point G

For point $G(-6,2)$, the new $x$ - coordinate is $x=-6 + 3=-3$, and the new $y$ - coordinate is $y=2 + 3=5$. So the new point $G'$ is $(-3,5)$.

Step7: Graph the new rectangle

Plot the points $D'(-3,-5)$, $E'(5,-5)$, $F'(5,5)$, $G'(-3,5)$ on the coordinate - plane and connect them in order to form the new rectangle.

Answer:

Graph the rectangle with vertices $D'(-3,-5)$, $E'(5,-5)$, $F'(5,5)$, $G'(-3,5)$ on the given coordinate grid.