Question

current skill $\\$ triangle npq was dilated to form triangle tuv. note: figures not drawn to scale. what scale factor was used for this dilation?

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of a side in the image}}{\text{length of the corresponding side in the pre - image}}\)

Step2: Identify corresponding sides

Let's take the sides \(TU\) (in the image triangle \(TUV\)) and \(NP\) (in the pre - image triangle \(NPQ\)). \(TU = 24\space mm\) and \(NP=12\space mm\)

Step3: Calculate the scale factor

Substitute the values into the formula: \(k=\frac{TU}{NP}=\frac{24}{12} = 2\)

We can check with another pair of corresponding sides. Let's take \(TV\) and \(NQ\). \(TV = 32\space mm\) and \(NQ = 16\space mm\). Then \(k=\frac{TV}{NQ}=\frac{32}{16}=2\)

Answer:

\(2\)