Question 175896
What are the coordinates of Parallelogram WXYZ; w(-1,2), X(3,3), Y(0,-4), and Z(-4,-4), reflected over the y-axis then rotated 180 degrees about the origin?
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Let's draw the parallelogram:

It's not a parallelogram. It's just a quadrilateral.
Did you maybe type the point X wrong, and it should 
be X(3,2) and not X(3,3)? But whatever, the principle 
is the same.  I'll just reflect and rotate
the quadrilateral.

{{{drawing(400,400,-5,5,-5,5, 
graph(400,400,-5,5,-5,5),
line(-1,2,3,3),
line(0,-4,3,3),
line(0,-4,-4,-4),
line(-1,2,-4,-4),


locate(-2.5,2.4,"W(-1,2)"),locate(3.1,3,X(3,3)), locate(-4,-4,"Z(-4,-4)"),locate(0.2,-4,Y(0,-4)) 

 )}}}

First we reflect it over the y-axis, by changing
the signs of the only the x-component.  It will 
now become quadrilateral ABCD

w(-1,2) becomes A(1,2) 
X(3,3) becomes B(-3,3) 
Y(0,-4) becomes C(0,-4) 
Z(-4,-4) becomes D(4,-4) 


{{{drawing(400,400,-5,5,-5,5, 
graph(400,400,-5,5,-5,5),
line(1,2,-3,3),
line(0,-4,-3,3),
line(0,-4,4,-4),
line(1,2,4,-4),


locate(1.3,2.4,"A(1,2)"),locate(-4.1,3,"B(3,3)"), locate(3.8,-4,"D(4,-4)"),locate(0.2,-4,"C(0,-4)") 

 )}}}

Now we rotate it 180° about the origin, by changing
the signs of both coordinates. It will now become
quadrilateral PQRS:

A(1,2) becomes P(-1,-2) 
B(-3,3) becomes Q(3,-3) 
C(0,-4) becomes R(0,4) 
D(4,-4) becomes S(-4,4)

{{{drawing(400,400,-5,5,-5,5, 
graph(400,400,-5,5,-5,5),
line(-1,-2,3,-3),
line(0,4,3,-3),
line(0,4,-4,4),
line(-1,-2,-4,4),


locate(-2,-2.1,"P(-1,-2)"),locate(3.2,-3,"Q(3,-3)"), locate(-4.5,4.5,"S(-4,4)"),locate(.2,4.5,"R(0,4)") 

 )}}}

Edwin</pre>