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