Question

record the coordinates of the reflected points.
original point points after reflection over x - axis
q (1,1) q ( , )
r (1,5) r ( , )
s (3,7) s ( , )
t (3,1) t ( , )

Explanation:

Step1: Recall reflection rule

When reflecting a point $(x,y)$ over the $x - axis$, the $x$-coordinate remains the same and the $y$-coordinate changes its sign. That is, the transformation is $(x,y)\to(x, - y)$.

Step2: Reflect point Q

For point $Q(1,1)$, applying the rule $(x,y)\to(x, - y)$, we get $Q'(1,-1)$.

Step3: Reflect point R

For point $R(1,5)$, applying the rule $(x,y)\to(x, - y)$, we get $R'(1,-5)$.

Step4: Reflect point S

For point $S(3,7)$, applying the rule $(x,y)\to(x, - y)$, we get $S'(3,-7)$.

Step5: Reflect point T

For point $T(3,1)$, applying the rule $(x,y)\to(x, - y)$, we get $T'(3,-1)$.

Answer:

Original Point	Points after reflection over x - axis
R $(1,5)$	R' $(1,-5)$
S $(3,7)$	S' $(3,-7)$
T $(3,1)$	T' $(3,-1)$