Answer:
Scale factor = 7
Step-by-step explanation:
Dilation with scale factor to map HEFG to DABC will be,
Scale factor = [tex]\frac{\text{Dimension of Image DABC}}{\text{Dimension of preimage HEFG}}[/tex]
= [tex]\frac{\text{Length of CD}}{\text{Length of GH}}[/tex]
Length of CD = Distance between two points C(0, -7) and D(-7, 0)
= [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
= [tex]\sqrt{(-7-0)^2+(0+7)^2}[/tex]
= [tex]\sqrt{98}[/tex]
= [tex]7\sqrt{2}[/tex]
Length of GH = Distance between G(0, -1) and H(-1, 0)
= [tex]\sqrt{(-1-0)^2+(0+1)^2}[/tex]
= [tex]\sqrt{2}[/tex]
Scale factor = [tex]\frac{7\sqrt{2} }{\sqrt{2} }[/tex]
= 7
