Question

figure qrst is dilated to form its image, figure qrst.
what is the scale factor of the dilation?
scale factor =
is point a the center of dilation?
is point q the center of dilation?

Explanation:

Step1: Determine the scale factor

Let's assume we can use the distance between corresponding points. For example, if we consider the length of a side. Suppose the length of \(RS\) is \(3\) units and the length of \(R'S'\) is \(6\) units. The scale factor \(k\) is given by the formula \(k=\frac{\text{length of image segment}}{\text{length of original segment}}\). So \(k = \frac{6}{3}=2\).

Step2: Check the center of dilation

For a dilation, the center of dilation is a fixed point. If we check the lines connecting corresponding points (e.g., \(R\) to \(R'\), \(S\) to \(S'\), \(T\) to \(T'\)). All these lines pass through point \(Q\). So point \(Q\) is the center of dilation.

Answer:

scale factor \(= 2\); Is point \(A\) the center of dilation? no; Is point \(Q\) the center of dilation? yes