Answercounterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axisexplanationthe given figure has vertices
![p(1,2),q(2,1),r(3,2),s(3,3)](/tex.php?f=p(1,2),q(2,1),r(3,2),s(3,3))
recall that for counterclockwise rotation about the origin,
![(x,y)\rightarrow (-x,-y)](/tex.php?f=(x,y)\rightarrow (-x,-y))
when we rotate figure pqrs counterclockwise through an angle of 180° about the origin, the coordinates will become
![p1( - 1, - 2),q1( - 2, - 1),r1( - 3, - 2),s1( - 3, - 3)](/tex.php?f=p1( - 1, - 2),q1( - 2, - 1),r1( - 3, - 2),s1( - 3, - 3))
next, we reflect in the y-axis by negating the x-coordinates of the resulting figure to obtain,
![p'(1, - 2),q'(2, - 1),r'(3, - 2),s'(3, - 3)](/tex.php?f=p'(1, - 2),q'(2, - 1),r'(3, - 2),s'(3, - 3))
therefore the correct answer is c