Question

which rotation is shown in the coordinate plane? 90° clockwise 90° counterclockwise 180° clockwise image of coordinate plane with two quadrilaterals, one in upper right and one in lower left, with labeled points p, q, r, s and p, q, r, s

Explanation:

Step1: Identify key points

Original points: $P(2,3)$, $Q(4,2)$, $R(4,-1)$, $S(1,2)$
Image points: $P'(-2,-3)$, $Q'(-4,-2)$, $R'(-4,1)$, $S'(-1,-2)$

Step2: Match rotation rule

Check 180° rotation rule: $(x,y)\to(-x,-y)$
For $P(2,3)$: $(-2,-3)=P'$
For $Q(4,2)$: $(-4,-2)=Q'$
For $R(4,-1)$: $(-4,1)=R'$
For $S(1,2)$: $(-1,-2)=S'$
All points fit this rule.

Answer:

180° clockwise