Question

If the model is 18 inches long and the actual locomotive is 72 feet long, what is the similarity transformation to map from the model to the actual locomotive? Express the answer using the notation x* ax, where x is a measurement on the model and ax is the corresponding measurement on the actual locomotive.

Answer 1

(1/48)ax

Explanation:

We can use the proportion of the lengths of the model and the actual locomotive to determine the scale factor for this similarity transformation.

The model is 18 inches long, which is equivalent to 1.5 feet (since 1 foot = 12 inches). The actual locomotive is 72 feet long. So, the scale factor can be calculated as:

scale factor = actual length / model length

scale factor = 72 feet / 1.5 feet

scale factor = 48

This means that each measurement on the model is 1/48th the size of the corresponding measurement on the actual locomotive. We can express this similarity transformation using the notation x* ax as: x* (1/48)ax

So, if a measurement on the model is x, the corresponding measurement on the actual locomotive would be (1/48)ax.