Question

given △ksl as the pre - image and △xwy as the image with the origin as the center of dilation, complete the statement. the scale factor of this dilation is <to find the scale factor, compare the coordinates of point <and point <the scale

Explanation:

Step1: Identify corresponding points

Let's take point \(W(1,2)\) as a point on the pre - image and point \(S(1,4)\) as the corresponding point on the image. Since the center of dilation is the origin \((0,0)\), the scale factor \(k\) for the \(y\) - coordinate (we can also use the \(x\) - coordinate, but here we use \(y\) for example) is calculated by the formula \(k=\frac{y_{image}}{y_{pre - image}}\).

Step2: Calculate the scale factor

For the \(y\) - coordinates of \(W\) and \(S\), \(y_{pre - image}=2\) and \(y_{image}=4\). So \(k = \frac{4}{2}=2\).

Answer:

2