Question

CHECK MY WORK PLEASE
graph the image of this figure after a dilation with a scale factor of 2 centered at the origin. Use the polygon tool to graph the dilated figure

Answer 1

Your scaling in the x direction is OK, but you didn't scale in the y direction properly. Hint. Scale each vertex of the original rectangle independently to construct the scaled rectangle.
I see the original points and their scaling by 2 as
(2,2) - Scales to (2*2, 2*2) = (4,4) OK in your drawing.
(-2,2) - Scales to (-2*2, 2*2) = (-4,4) OK in your drawing.
(2,5) - Scales to (2*2, 5*2) = (4,10) Error in your drawing.
(-2,5) - Scales to (-2*2, 5*2) = (-4,10) Error in your drawing.

Answer 2

Rectangle with vertexes of (4,4), (-4,4), (4,10), and (-4,10)
   I can't do your graph for you, but I can help with the coordinates of the final polygon. In general to scale (x,y) by s centered at (a,b) that would mean that (x,y) maps to ((x-a)*s+a, (y-b)*s+b). And since we've been given (a,b) = (0,0), the mapping simplifies to (x,y) maps to (x*s, y*s). So let's do it:

   Point (2,2) ==> (2*2,2*2) = (4,4)
 Point (-2,2) ==> (-2*2,2*2) = (-4,4)
 Point (2,5) ==> (2*2,5*2) = (4,10)
 Point (-2,5) ==> (-2*2,5*2) = (-4,10)
   So your desired polygon is a rectangle with vertexes of (4,4), (-4,4), (4,10), and (-4,10)