Question

1. 180° rotation

Explanation:

Step1: Recall 180 - degree rotation rule

For a 180 - degree rotation about the origin, the transformation rule for a point $(x,y)$ is $(x,y)\to(-x,-y)$.

Step2: Identify coordinates of points

From the graph, we have $P(-4,0)$, $Q(-1,0)$, $R(-1,4)$, $S(-4,4)$.

Step3: Apply rotation rule to point P

For $P(-4,0)$, using the rule $(x,y)\to(-x,-y)$, we get $P'(4,0)$.

Step4: Apply rotation rule to point Q

For $Q(-1,0)$, we get $Q'(1,0)$.

Step5: Apply rotation rule to point R

For $R(-1,4)$, we get $R'(1, - 4)$.

Step6: Apply rotation rule to point S

For $S(-4,4)$, we get $S'(4,-4)$.

Answer:

$P'(4,0)$
$Q'(1,0)$
$R'(1,-4)$
$S'(4,-4)$