Answer:
The scale factor was used in the dilation is 3
Step-by-step explanation:
Dilation is a kind of transformation that changes the size of figures
Image of a figure by dilation and the figure are similar
If a triangle dilated by a scale factor k then its image is similar to it, and the constant ratio between their corresponding sides is equal to k
∵ Δ ABC is dilated to form Δ DEF
∴ Δs ABC and DEF are similar
- That mean their corresponding sides have constant ratio
equal the scale factor of dilation
∴ [tex]\frac{DE}{AB}=\frac{EF}{BC}=\frac{DF}{AC}=k[/tex]
Size of Δ DEF is greater than size of Δ ABC, that means k > 1
∵ AC = 2 units
∵ DF = 6 units
∵ [tex]\frac{DF}{AC}=k[/tex]
∴ [tex]\frac{6}{2}=k[/tex]
∴ 3 = k
∵ The scale factor of dilation is equal to the constant ratio k
∵ k = 3
∴ The scale factor was used in the dilation is 3
