Chapter 12.7, Problem 3C

To determine

To find:the scale factor

Answer to Problem 3C

The scale factor is 6

Explanation of Solution

Given information: $\overline{AB}$ with end points $A\left(0.5,1\right)\text{ and }B\left(1.5,1\right)$ and the image of $\overline{AB}$ is $\overline{A\text{'}B\text{'}}$ with the end points $A\text{'}\left(3,6\right)\text{ and }B\text{'}\left(9,6\right)$

Calculation:

first draw $\overline{AB}$ with end points $A\left(0.5\right)\text{ and }B\left(1.5,1\right)$ and the image of $\overline{AB}$ is $\overline{A\text{'}B\text{'}}$ with the end points $A\text{'}\left(3,6\right)\text{ and }B\text{'}\left(9,6\right)$

Original	Image
$\overline{AB}$	$\overline{A\text{'}B\text{'}}$
$A\left(0.5,1\right)$	$A\text{'}\left(3,6\right)$
$B\left(1.5,1\right)$	$B\text{'}\left(9,6\right)$

Finally draw a line $\overline{A\text{'}B\text{'}}$ , as shown below

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:

  $\begin{array}{l}k=\frac{xA\text{'}}{xA}\\ =\frac{3}{0.5}\\ \text{ = 6 }\left[\text{divide}\right]\end{array}$