The correct statement is that △Q'C'' ' is obtained by reflecting △QCX over the y-axis and then dilating it about the origin by a scale factor D of 3/2.
To determine which statement can be used to prove that △QCX is similar to △Q'C'C'X, we need to examine the transformations applied to each triangle.
Let's analyze the given information:
△Q'C'X is obtained by reflecting △QCX over the y-axis and then dilating it about the origin by a scale factor A of 2/3.
△Q'C'' is obtained by reflecting △QCX over the x-axis and then dilating it about the origin by a scale factor B of 3/2.
Now, we want to find the transformation for △Q'C'' '.
△Q'C'' ' is obtained by reflecting △QCX over the y-axis and then dilating it about the origin by a scale factor D of 3/2.
To prove that △QCX is similar to △Q'C'C'X, we need to show that the ratios of corresponding sides are equal. Since the transformations involve reflections and dilations, the scale factors are crucial.
Let's compare the scale factors:
A = 2/3
B = 3/2
D = 3/2
The statement that matches the transformations and scale factors is:
△Q'C'' ' is obtained by reflecting △QCX over the y-axis and then dilating it about the origin by a scale factor D of 3/2.
Therefore, the correct statement is that △Q'C'' ' is obtained by reflecting △QCX over the y-axis and then dilating it about the origin by a scale factor D of 3/2.