Question

k = 4
k = 1/4
k = 2
k = 1/2
k = 6
k = 1/3

Explanation:

Step1: Identify corresponding points

Let's assume a point on the pre - image and its corresponding point on the image. For example, if we consider the vertical distance of a point from the x - axis. Suppose the y - coordinate of a point on the pre - image is \(y\) and on the image is \(y'\). The scale factor \(k\) for a dilation is given by the ratio of the coordinates of the image to the pre - image. Let's take point \(S\) and \(S'\). If we assume the coordinates of \(S\) are \((4,10)\) and of \(S'\) are \((4, 5)\).

Step2: Calculate the scale factor

The scale factor \(k=\frac{y'}{y}\). Here, \(y' = 5\) and \(y = 10\), so \(k=\frac{5}{10}=\frac{1}{2}\).

Answer:

\(k = 1/2\)