Answer:
Image was reduced by a scale factor = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Since, segment A'B' is the image of segment AB,
Scale factor = [tex]\frac{\text{Length of image}}{\text{Length of actual}}[/tex]
= [tex]\frac{A'B'}{AB}[/tex]
Length of AB = [tex]\sqrt{(BB')^2+(AB')^2}[/tex] [By Pythagoras theorem]
= [tex]\sqrt{2^2+4^2}[/tex]
= [tex]\sqrt{20}[/tex]
= [tex]2\sqrt{5}[/tex]
Length of A'B' = [tex]\sqrt{1^2+2^2}[/tex]
= [tex]\sqrt{5}[/tex]
Scale factor = [tex]\frac{\sqrt{5} }{2\sqrt{5} }[/tex]
= [tex]\frac{1}{2}[/tex]
Therefore, image AB has been reduced by a scale factor of [tex]\frac{1}{2}[/tex]
