If ABC ~ DEF and the scale factor from ABC to DEF is 1/6, what are the lengths of DE,EF , and DF, respectively?

I'd say they are 1/66 times the lengths of AB,BC,CA respectively.

If ABC ~ DEF and the scale factor from ABC to DEF is 3/4, what is the lengths of Df?

If ABC ~ DEF and the scale factor from ABC to DEF is 1/6, it means that the corresponding sides of the two triangles are proportional.

Let's assume that the length of side AB is "x". Since the scale factor is 1/6, the length of corresponding side DE would be (1/6) * x.

Therefore, the length of side DE is (1/6) * x.

Similarly, if the length of side BC is "y", the length of corresponding side EF would be (1/6) * y.

Therefore, the length of side EF is (1/6) * y.

Finally, if the length of side AC is "z", the length of corresponding side DF would be (1/6) * z.

Therefore, the length of side DF is (1/6) * z.

In summary, the lengths of DE, EF, and DF are (1/6) * x, (1/6) * y, and (1/6) * z, respectively.

To find the lengths of DE, EF, and DF, we need to use the scale factor. The scale factor is a ratio that relates corresponding lengths of similar figures.

In this case, the scale factor from ABC to DEF is 1/6. This means that the corresponding lengths of corresponding sides are in the ratio of 1/6.

Let's say the length of side AB is x. To find the length of DE, we can multiply the scale factor by the length of AB: DE = (1/6) * AB = (1/6) * x = x/6.

Similarly, we can find the lengths of EF and DF:
EF = (1/6) * BC = (1/6) * x = x/6,
DF = (1/6) * AC = (1/6) * x = x/6.

Therefore, the lengths of DE, EF, and DF are all x/6.