Chapter 12.7, Problem 28E

To determine

To find:the scale factor

Answer to Problem 28E

G. $k=\frac{1}{2}$

Explanation of Solution

Given information: $ABCD$ is a quadrilateral and the image of quadrilateral is $A\text{'}B\text{'}C\text{'}D\text{'}$ after the dilation

Data from the figure;

$\begin{array}{l}A=\left(-4,-4\right)\\ A\text{'}=\left(-2,-2\right)\end{array}$

Dilation is given by $\left(x,y\right)\to \left(kx,ky\right)$ , so evaluate the scale factor of dilation by taking the ratio of any set of corresponding co ordinates,here the ratio of $\frac{xA\text{'}}{xA}$ is evaluated;

Therefore, the Scale factor is:

  $\begin{array}{l}k=\frac{xA\text{'}}{xA}\\ =\frac{2}{-4}\\ \text{ = }\frac{1}{2}\left[\text{divide}\right]\end{array}$

Hence, the correct answer is G. $k=\frac{1}{2}$