SOLUTION: 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?

Algebra ->  Algebra  -> Parallelograms -> SOLUTION: 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?      Log On

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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?
Answer by Edwin McCravy(6936) About Me  (Show Source):
You can put this solution on YOUR website!
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?

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%28400%2C400%2C-5%2C5%2C-5%2C5%2C+%0D%0Agraph%28400%2C400%2C-5%2C5%2C-5%2C5%29%2C%0D%0Aline%28-1%2C2%2C3%2C3%29%2C%0D%0Aline%280%2C-4%2C3%2C3%29%2C%0D%0Aline%280%2C-4%2C-4%2C-4%29%2C%0D%0Aline%28-1%2C2%2C-4%2C-4%29%2C%0D%0A%0D%0A%0D%0Alocate%28-2.5%2C2.4%2C%27W%28-1%2C2%29%27%29%2Clocate%283.1%2C3%2CX%283%2C3%29%29%2C+locate%28-4%2C-4%2C%27Z%28-4%2C-4%29%27%29%2Clocate%280.2%2C-4%2CY%280%2C-4%29%29+%0D%0A%0D%0A+%29

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%28400%2C400%2C-5%2C5%2C-5%2C5%2C+%0D%0Agraph%28400%2C400%2C-5%2C5%2C-5%2C5%29%2C%0D%0Aline%281%2C2%2C-3%2C3%29%2C%0D%0Aline%280%2C-4%2C-3%2C3%29%2C%0D%0Aline%280%2C-4%2C4%2C-4%29%2C%0D%0Aline%281%2C2%2C4%2C-4%29%2C%0D%0A%0D%0A%0D%0Alocate%281.3%2C2.4%2C%27A%281%2C2%29%27%29%2Clocate%28-4.1%2C3%2C%27B%283%2C3%29%27%29%2C+locate%283.8%2C-4%2C%27D%284%2C-4%29%27%29%2Clocate%280.2%2C-4%2C%27C%280%2C-4%29%27%29+%0D%0A%0D%0A+%29

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%28400%2C400%2C-5%2C5%2C-5%2C5%2C+%0D%0Agraph%28400%2C400%2C-5%2C5%2C-5%2C5%29%2C%0D%0Aline%28-1%2C-2%2C3%2C-3%29%2C%0D%0Aline%280%2C4%2C3%2C-3%29%2C%0D%0Aline%280%2C4%2C-4%2C4%29%2C%0D%0Aline%28-1%2C-2%2C-4%2C4%29%2C%0D%0A%0D%0A%0D%0Alocate%28-2%2C-2.1%2C%27P%28-1%2C-2%29%27%29%2Clocate%283.2%2C-3%2C%27Q%283%2C-3%29%27%29%2C+locate%28-4.5%2C4.5%2C%27S%28-4%2C4%29%27%29%2Clocate%28.2%2C4.5%2C%27R%280%2C4%29%27%29+%0D%0A%0D%0A+%29

Edwin