Question

Draw the dilation image A'B'C'D' of the trapezoid ABCD with the center of the dilation at the origin and the scale factor -2.

Answer 1

An enlargement with a negative scale factor enlarges a shape so it is on the other side of the center of enlargement. The trapezoid will appear rotated by 180° as well as twice enlarged.
The trapezoid ABCD has vertices ar points A(-4,-1), B(-1,-1), C(0,-5) and D(-5,-5).  Thus, the trapezoid A'B'C'D' has vertices at points A'(8,2), B'(2,2), C'(0,10) and D'(10,10).

Answer 2

The coordinates of the trapezoid ABCD

A(-4,-1) , B(-1,-1) , C(0,-5) and (-5,-5)

The dilation at the origin and the scale factor -2.

So, the rule will be ⇒ (x,y)→(-2x,-2y)
So, A(-4,-1) ⇒⇒⇒ A'(8,2)
      B(-1,-1) ⇒⇒⇒ B(2,2)
      C(0,-5) ⇒⇒⇒ C'(0,10)
      D(-5,-5) ⇒⇒⇒ D'(10,10)


See the attached figure .