Question

A graphic designer created a logo on 8 1/2 by 11 inch paper. In order to place on a business card the logo needs to be 1 7/10 inches by 2 1/5. What is the scale factor of the dilation?

Answer 1

K  - scale factor
a = 8 1/2
b = 11
a₁ = 1 7/10
b₁ = 2 1/5


$k = \frac{a_1}{a}=\frac{b_1}b\\\\\\\frac{a_1}{a}=\dfrac{1 \frac{7}{10}}{8\frac12}=1 \frac{7}{10}:8\frac12=\frac{17}{10}:\frac{17}2=\frac{17}{10}\cdot\frac2{17}=\frac15\cdot\frac11=\frac15\\\\\\\frac{b_1}{b}=\dfrac{2 \frac{1}{5}}{11}=2\frac15:11=\frac{11}{5}\cdot\frac1{11}=\frac15\cdot\frac11=\frac15 \\\\\\\frac{a_1}{a}=\frac{b_1}b=\frac15\ \ \ \implies\ \ \ k=\frac15$