Answer:
Dilation is done by the scale factor of Five-halves.
Step-by-step explanation:
Please refer to the image attached,
The graph clearly shows the triangles [tex]\triangle[/tex]ABC and [tex]\triangle[/tex]A'B'C'.
Let us calculate the sides of triangles first then we will be able to find scale factor of dilation.
Using the distance formula:
Distance between 2 points [tex]P (x_1,y_1) \text{ and } Q (x_2,y_2)[/tex] is given by formula:
PQ = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Side AB is along x-axis, side AB =
[tex]\sqrt{(2-0)^2+(2-2)^2}\\\Rightarrow \sqrt{4}\\\Rightarrow 2\ units[/tex]
Similarly side, BC = 2 units
Now, in [tex]\triangle[/tex]A'B'C', A'B' can be calculated by distance formula:
[tex]\sqrt{(1+4)^2+(-1- (-1))^2}\\\Rightarrow \sqrt{25}\\\Rightarrow 5\ units[/tex]
B'C' = 5 units
The ratio of sides:
AB : A'B' = 2:5
[tex]\Rightarrow \dfrac{AB}{A'B'} = \dfrac{2}{5}\\\Rightarrow A'B' = \dfrac{5}{2} AB[/tex]
So, scaling factor is [tex]\dfrac{5}{2}[/tex] or 2.5.
OR
Scaling factor is Five-halves.
