The length of image of AB after the dilation is 18 cm
Solution:
Given data:
Length of AB = 9 cm
Scale factor (k) = 2
Length of image of AB = ?
By the definition of scale factor,
![$k=\frac{\text { Length of Dilated image AB }}{\text { Length of original image } \mathrm{AB}}$](https://img.qammunity.org/2021/formulas/mathematics/middle-school/19p4pd95001u94l8p4dt0ot5d9s5vxecsa.png)
![$2=\frac{\text { Length of Dilated image AB }}{9}](https://img.qammunity.org/2021/formulas/mathematics/middle-school/k396uxelzhde5d3xran98o4gavz76aaiyt.png)
Do cross multiplication, we get
2 × 9 = Length of dilated image of AB
18 = Length of dilated image of AB
Hence the length of image of AB after the dilation is 18 cm.