Answer:
[tex](x,y) => (2.5x,2.5y)[/tex]
Step-by-step explanation:
Given
See attachment for ABCD and A'B'C'D'
Required
Determine the dilation rule
Using AB and A'B' as points of references;
[tex]AB = (-1,2)\ to\ (2,1)[/tex]
[tex]A'B' = (-2.5,5)\ to\ (5,2.5)[/tex]
The dilation factor (k) is calculated as:
[tex]k = \frac{A'B'}{AB}[/tex]
This gives:
[tex]k = \frac{(-2.5,5)}{(-1,2)} \ or\ k = \frac{(5,2.5)}{(2,1)}[/tex]
Factorize
[tex]k = \frac{2.5*(-1,2)}{(-1,2)} \ or\ k = \frac{2.5*(2,1)}{(2,1)}[/tex]
[tex]k = 2.5 \ or\ k = 2.5[/tex]
Hence, the scale factor is 2.5
The dilation rule is:
[tex](x,y) => k(x,y)[/tex]
[tex](x,y) => 2.5(x,y)[/tex]
[tex](x,y) => (2.5x,2.5y)[/tex]
