Chapter SH, Problem 6.8.3EP

To determine

To calculate: To find the scale factor of dilation

Answer to Problem 6.8.3EP

Scaling factor of dilation is $1.5$

Explanation of Solution

Given information: A $3\frac{1}{2}$ inch by $2$ inch business card is being enlarged to $5\frac{1}{4}$ inch by $3$ inch to use as an advertisement

Formula Used:

Dilation is an enlargement or reduction of any object by a scale factor

Let scale factor be $k$

Thus, new coordinate of point $\left(x,y\right)$ after dilation is given as

  $\left(kx,ky\right)$

Calculation:

Given that a $3\frac{1}{2}$ inch by $2$ inch business card is being enlarged to $5\frac{1}{4}$ inch by $3$ inch to use as an advertisement

Scale factor of dilation is calculated

  $\begin{array}{l}scale=\frac{5\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}{3\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\\ scale=\frac{\raisebox{1ex}{$21$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}{\raisebox{1ex}{$7$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\\ scale=\frac{21\times 2}{7\times 4}\\ scale=\frac{3\times 1}{1\times 2}\\ scale=1.5\end{array}$

Conclusion:

Hence, scaling factor of dilation is $1.5$