Question

Point O is the center of dilation. Triangle DEF is dilated to create a smaller triangle D' E' F'. The length of OF' is 3. The length of FF' is 7. What is the scale factor of the dilation of triangle DEF?

Answer 1

The scale factor for the dilation of triangle DEF is 0.3, found by dividing the length of OF' by the total length of OF' plus FF' (3/10).

Step-by-step explanation:

The student has asked how to find the scale factor of the dilation of triangle DEF, given that the length of OF' is 3 and the length of FF' is 7. The scale factor can be found using the ratio of OF' to the sum of OF' and FF', since OF' is the distance from the center of dilation to the dilated point, and OF' plus FF' gives us the distance from the center of dilation to the original point. Hence, the scale factor k is OF' / (OF' + FF').

Now, we plug in the given values:

• OF' = 3
• FF' = 7

The calculation will be as follows:

Scale Factor, k = OF' / (OF'+ FF') = 3 / (3 + 7) = 3 / 10 = 0.3

Therefore, the scale factor for the dilation is 0.3, meaning that triangle D'E'F' is three-tenths the size of triangle DEF.