Question

Question 4 (5 points)

Answer 1

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

∴ $\frac{DE}{AB}=\frac{EF}{BC}=\frac{DF}{AC}=k$

Size of Δ DEF is greater than size of Δ ABC, that means k > 1

∵ AC = 2 units

∵ DF = 6 units

∵ $\frac{DF}{AC}=k$

∴ $\frac{6}{2}=k$

∴ 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