How do I put a scale factor of a pre image and image into a ratio

Question

There is a question where I can look at a diagram which shows me two triangles and asks if the dilation is an enlargement or reduction (I understand how to figure that out) but it also asks me to determine the scale factor but the place to answer the scale factor looks like this __:__ which is for a ratio... So how do I make the scale factor a ratio??

Answer 1

suppose that your diagram shows two SIMILAR triangles and that the one on the left has longest side 12 and the triangle on the right (of the diagram) has CORRESPONDING side 7.

 

Then the ratio of 12:7 applies, i.e. to go from the triangle on the left to the triangle on the right by applying a scale factor, corresponding lengths of the triangle on the right would be multiplied by a scale factor 7/12 to REDUCE them appropriately.

 

On the other hand, to go from the smaller triangle (on the right of the diagram), the scale factor 12/7 would be applied, to increase corresponding side lengths appropriately.