Question

graph the image of rhombus stuv after a translation 8 units right and 8 units up.

Explanation:

Step1: Recall translation rule

For a point $(x,y)$ translated 8 units right and 8 units up, the new - point is $(x + 8,y + 8)$.

Step2: Identify original coordinates

Let's assume the coordinates of the vertices of rhombus $STUV$ are $S(x_1,y_1)$, $T(x_2,y_2)$, $U(x_3,y_3)$, $V(x_4,y_4)$. From the graph, if $S(-2,-9)$, $T(-2,-4)$, $U(1,-2)$, $V(1,-6)$.

Step3: Calculate new coordinates

For point $S$: $x_1=-2,y_1 = - 9$, new coordinates are $S'(-2 + 8,-9 + 8)=(6,-1)$.
For point $T$: $x_2=-2,y_2=-4$, new coordinates are $T'(-2 + 8,-4 + 8)=(6,4)$.
For point $U$: $x_3 = 1,y_3=-2$, new coordinates are $U'(1 + 8,-2 + 8)=(9,6)$.
For point $V$: $x_4 = 1,y_4=-6$, new coordinates are $V'(1 + 8,-6 + 8)=(9,2)$.

Step4: Graph the new rhombus

Plot the points $S'(6,-1)$, $T'(6,4)$, $U'(9,6)$, $V'(9,2)$ on the same coordinate - plane and connect them in order to get the image of rhombus $STUV$ after the translation.

Answer:

Graph the points $S'(6,-1)$, $T'(6,4)$, $U'(9,6)$, $V'(9,2)$ and connect them to form the new rhombus.