Question

use the graph to answer questions 9 - 11. 9. reflect figure opqr over the x - axis. record the coordinates for p’. (-3,-2) 10. translate figure stuv 7 units down and 5 units left. record the coordinates for t’. (-1,0)

Explanation:

Step1: Recall reflection rule

When reflecting a point $(x,y)$ over the $x - axis$, the rule is $(x,y)\to(x, - y)$. Assume the coordinates of point $P$ are $(x,y)$.

Step2: Identify $P$ coordinates

From the graph, assume the coordinates of point $P$ are $(-3,2)$.

Step3: Apply reflection rule

Using the rule $(x,y)\to(x, - y)$, for $P(-3,2)$ reflected over the $x - axis$, we get $P'(-3,-2)$.

Step4: Recall translation rule

For a translation of a point $(x,y)$ 7 units down and 5 units left, the rule is $(x,y)\to(x - 5,y - 7)$. Assume the coordinates of point $T$ are $(x,y)$.

Step5: Identify $T$ coordinates

From the graph, assume the coordinates of point $T$ are $(4,7)$.

Step6: Apply translation rule

Using the rule $(x,y)\to(x - 5,y - 7)$, for $T(4,7)$ we have $x=4,y = 7$. Then $x-5=4 - 5=-1$ and $y - 7=7 - 7 = 0$. So $T'(-1,0)$.

Answer:

1. (-3,-2)
2. (-1,0)