3
Step-by-step explanation:
The equation of line passing through the two points is [tex]\frac{y-y_{1} }{x-x_{1} }=\frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex]
When substituted,the equation becomes [tex]\frac{y-6}{x-2}=\frac{18-6}{6-2}[/tex]
which when simplified is [tex]y=3\times x[/tex]
The line clearly passes through origin.
The distance between two points is [tex]\sqrt{(y_{1}-y_{2} )^{2}+(x_{1}- x_{2} )^{2}}[/tex]
Distance between origin and [tex](2,6)[/tex] is [tex]\sqrt{40}[/tex].
Distance between origin and [tex](6,18)[/tex] is [tex]\sqrt{360}[/tex]
Scale factor is [tex]\frac{distance\text{ }of\text{ }p_{2}\text{ from origin}}{distance \text{ } of \text{ } p_{1}\text{ from origin}}[/tex]
So,scale factor is [tex]\frac{\sqrt{360} }{\sqrt{40} }[/tex]
which when simplified becomes 3.
