Answer:
Options A, B, D and E are true.
Step-by-step explanation:
In the figure attached, trapezoid ABCD is dilated to create trapezoid A'B'C'D'.
Option A.
Length of AD = Distance of A from the origin + Distance of D from the origin
= 4 + 4
= 8 units
Option A is true.
Option B.
Length of A'D' = Distance of A' from the origin + distance of D' from the origin
= 2 + 2
= 4 units
Option B is true.
Option C.
As we have measured in the options A and option B
[tex]\frac{AD}{A'D'}=\frac{8}{4}[/tex]
AD = 2× A'D'
So image is smaller than the pre image after dilation.
Option C is not true.
Option D.
Since coordinates of C and D are (2, 4) and (4, 0)
so the slope of CD = [tex]\frac{y-y'}{x-x'}[/tex]
= [tex]\frac{4-0}{2-4}[/tex]
= [tex]\frac{4}{(-2)}[/tex]
= (-2)
Now we know coordinates of C' and D' are (1, 2) and (2, 0)
Then slope of C'D' = [tex]\frac{2-0}{1-2}[/tex]
= [tex]\frac{2}{-1}=(-2)[/tex]
Therefore, slopes of CD and C'D' are same.
Option D is True.
Option E.
Scale factor = [tex]\frac{A'D'}{AD}=\frac{4}{8}[/tex]
= [tex]\frac{1}{2}[/tex]
Option E is true.
Therefore, Options A, B, D and E are true.
