Question

scale factor:

Explanation:

Step1: Select corresponding points

Let's take point \(V(4,6)\) and \(V'(4, 12)\)

Step2: Calculate scale - factor for y - coordinates

The scale factor \(k\) for the y - coordinates is calculated as \(k=\frac{y_{V'}}{y_V}\)
\[k = \frac{12}{6}=2\]
We can also check with another set of corresponding points. Let's take \(W(6,2)\) and \(W'(10,2)\). The distance from the y - axis for \(W\) is \(6\) and for \(W'\) is \(10\). The scale factor for the x - coordinates is \(k=\frac{x_{W'}}{x_W}=\frac{10}{5} = 2\) (assuming the pre - image point for \(W'\) has \(x\) - coordinate \(5\) after proper identification of the pre - image). Since the scale factor is the same for both x and y directions, the overall scale factor is consistent.

Answer:

2