Question

graph the image of square rstu after a translation 7 units down.

Explanation:

Step1: Recall translation rule

For a translation 7 units down, the rule is $(x,y)\to(x,y - 7)$.

Step2: Identify original coordinates

Let's assume the coordinates of the vertices of square $RSTU$ are $R(x_1,y_1)$, $S(x_2,y_2)$, $T(x_3,y_3)$, $U(x_4,y_4)$. From the graph, if we assume $R(4,5)$, $S(6,5)$, $T(6,7)$, $U(4,7)$.

Step3: Apply the translation rule

For point $R$: $(4,5)\to(4,5 - 7)=(4,- 2)$.
For point $S$: $(6,5)\to(6,5 - 7)=(6,-2)$.
For point $T$: $(6,7)\to(6,7 - 7)=(6,0)$.
For point $U$: $(4,7)\to(4,7 - 7)=(4,0)$.

Step4: Graph the new - points

Plot the points $(4,-2)$, $(6,-2)$, $(6,0)$, $(4,0)$ on the coordinate plane and connect them to form the new square.

Answer:

Graph the square with vertices $(4,-2)$, $(6,-2)$, $(6,0)$, $(4,0)$.