Answer:
The 3rd graph represents the dilated image of the rectangle.
Step-by-step explanation:
We are given the rectangle having vertices,
(1,-2), (1,2), (-1,2) and (-1,-2).
Now, this rectangle is dilated about the origin by the scale factor of [tex]\frac{1}{2}[/tex]
That is, the size of the rectangle is reduced by the factor [tex]\frac{1}{2}[/tex].
Then, the vertices of the new rectangle will be,
(1,-2) changes to [tex]\frac{1}{2}\times (1,-2)[/tex] = [tex](\frac{1}{2},-1)[/tex]
(1,2) changes to [tex]\frac{1}{2}\times (1,2)[/tex] = [tex](\frac{1}{2},1)[/tex]
(-1,2) changes to [tex]\frac{1}{2}\times (-1,2)[/tex] = [tex](\frac{-1}{2},1)[/tex]
(-1,-2) changes to [tex]\frac{1}{2}\times (-1,-2)[/tex] = [tex](\frac{-1}{2},-1)[/tex]
So, the vertices of the dilated rectangle are [tex](\frac{1}{2},-1)[/tex], [tex](\frac{1}{2},1)[/tex], [tex](\frac{-1}{2},1)[/tex] and [tex](\frac{-1}{2},-1)[/tex].
Thus, the 3rd graph shown below represents the dilated image of the rectangle.
