Answer:
Point D is the point of dilation.
Step-by-step explanation:
If the smaller triangle A'B'C' is dilated to form a larger triangle ABC by the dilation about point D,
Ratio of the DA and DA' will be equal to the ratio of DB and DB'.
Length of DA = 3 units
Length of DA' = 1 unit
Coordinates of D → (3, 0)
Coordinates of B → (9, 3)
Coordinates of B' → (5, 1)
Use the formula of distance between the two points to find find the length of DB and DB'
Length of DB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(3-0)^2+(9-3)^2}[/tex]
[tex]=\sqrt{45}[/tex]
[tex]=3\sqrt{5}[/tex]
Length of DB' = [tex]\sqrt{(5-3)^2+(1-0)^2}[/tex]
[tex]=\sqrt{5}[/tex]
Ratio of DB and DB' = [tex]\frac{3\sqrt{5} }{\sqrt{5} } =3:1[/tex]
Ratio of DA and DA' = 3 : 1
Since, [tex]\frac{DA}{DA'}=\frac{DB}{DB'}[/tex]
Therefore, smaller triangle is dilated by a scale factor of 3 to form the bigger triangle about the point D.
