Question

in the diagram below, pq is the result of a dilation of pq. what is the scale - factor of the dilation? a. 2 b. $\frac{1}{3}$ c. 3 d. $\frac{1}{2}$

Explanation:

Step1: Identify corresponding lengths

Let's assume we consider the vertical distance from the x - axis to point P and P'. The y - coordinate of P is 4 and of P' is 2.

Step2: Calculate scale factor formula

The scale factor \(k\) of a dilation is given by the ratio of the length of the dilated segment to the original segment. For a point \((x,y)\) dilated to \((x',y')\), \(k=\frac{y'}{y}\) (when dilation is centered at the origin and considering vertical distances here). Here, \(k = \frac{2}{4}=\frac{1}{2}\).

Answer:

D. \(\frac{1}{2}\)