what is the scale factor of the dilation of triangle DEF?

Answer: First option 3/10
SolutionThe scale factor of dilation of triangle DEF is the ratio between the corresponding sides of the triangle D'E'F' and the triangle DEF:Scale factor: f=D'F'/DF=D'E'/DE=E'F'/EF (1)We can find the ratio D'F'/DF using the similar triangles OD'F' and ODF, because their sides must be proportionals:D'F'/DF=OF'/OF=OD'/OD (2)We know according with the figure:OF'=3 and F'F=7, then:OF=OF'+F'F→OF=3+7→OF=10Then replacing in (2):(2) D'F'/DF=3/10=OD'/ODAnd replacing in (1):(1) f=3/10=D'E'/DE=E'F'/EFAnswer: The scale factor of dilation of triangle DEF is 3/10