The quadrilateral ABCD is dilated at the center (0,0) with a scale factor of 1/2. So, after the dilation the length of A'B' is [tex]\sqrt{5}[/tex] and this can be determined by using the formula of length between two points.
Given :
- Quadrilateral ABCD is dilated at the center (0,0) with a scale factor of 1/2 to form quadrilateral A'B'C'D'.
- Points - A(0,4), B(4,2), C(4,-4), and D(-2,-2).
Given that the quadrilateral ABCD is dilated at the center (0,0) with a scale factor of 1/2. So the points of the quadrilateral ABCD becomes:
[tex]\rm A(0,4) \to A'(0\times \dfrac{1}{2},4\times \dfrac{1}{2}) = A'(0,2)[/tex]
[tex]\rm B(4,2) \to B'(4\times \dfrac{1}{2},2\times \dfrac{1}{2}) = B'(2,1)[/tex]
[tex]\rm C(4,-4) \to C'(4\times \dfrac{1}{2},-4\times \dfrac{1}{2}) = C'(2,-2)[/tex]
[tex]\rm D(-2,-2) \to D'(-2\times \dfrac{1}{2},-2\times \dfrac{1}{2}) = D'(-1,-1)[/tex]
Now, the length of A'B' is given by:
[tex]\rm AB=\sqrt{(4-0)^2+(2-4)^2}[/tex]
[tex]\rm AB=\sqrt{4^2+(-2)^2}[/tex]
[tex]\rm AB=\sqrt{20}[/tex]
[tex]\rm AB = 2\sqrt{5}[/tex]
[tex]\rm A'B' = \dfrac{1}{2}AB[/tex]
[tex]\rm A'B' = \sqrt{5}[/tex]
Therefore, the correct option is a).
For more information, refer to the link given below:
https://brainly.com/question/13911928
