Chapter 12.7, Problem 4E

To determine

To find:the scale factor

Answer to Problem 4E

The scale factor is 2.5

Explanation of Solution

Given information: $\overline{AB}$ with end points $A\left(-2,3\right)\text{ and }B\left(-2,-4\right)$ and the image of $\overline{AB}$ is $\overline{A\text{'}B\text{'}}$ with the end points $A\text{'}\left(-5,-7.5\right)\text{ and }B\text{'}\left(-5,-10\right)$

Calculation: first draw $\overline{AB}$ with end points $A\left(-2,3\right)\text{ and }B\left(-2,-4\right)$ and the image of $\overline{AB}$ is $\overline{A\text{'}B\text{'}}$ with the end points $A\text{'}\left(-5,-7.5\right)\text{ and }B\text{'}\left(-5,-10\right)$

Original	Image
$\overline{AB}$	$\overline{A\text{'}B\text{'}}$
$A\left(-2,3\right)$	$A\text{'}\left(-5,7.5\right)$
$B\left(-2,-4\right)$	$B\text{'}\left(-5,-10\right)$

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

  $\begin{array}{l}k=\frac{xA\text{'}}{xA}\\ =\frac{-5}{-2}\\ \text{ = 2}\text{.5 [divide] }\\ \end{array}$