Answer:Part a) [tex]\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}[/tex]Part b) The dilation is an enlargement, because the sides of the image are larger than the sides of the original figure.(the scale factor is greater than 1)Part c) The scale factor is [tex]3[/tex]Step-by-step explanation:Part a) Write the similarity statementwe know thatIf two figures are similar, then the ratio of its corresponding sides is equal so[tex]\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}[/tex]substitute the values[tex]\frac{9}{27}=\frac{12}{36} =\frac{15}{45}[/tex][tex]\frac{1}{3}=\frac{1}{3} =\frac{1}{3}[/tex] ----> is truethereforethe figures are similarPart b) The dilation is an enlargement, because the sides of the image are larger than the sides of the original figure. (the scale factor is greater than 1) Part c) we know thatIf two figures are similar, then the ratio of its corresponding sides is equal to the scale factorLetz------> the scale factorx-----> corresponding side of the imagey------> corresponding side of the original figureso[tex]z=\frac{x}{y}[/tex]we have[tex]x=A'B'=27\ units[/tex][tex]y=AB=9\ units[/tex]substitute[tex]z=\frac{27}{9}=3[/tex]The scale factor is greater than 1thereforeIs an enlargement