Question

a flea is 0.2 cm long. as it walkes across the glass surface of an overhead projector, its image on the screen appears 4cm long. what is the scale factor of the dialation? if the flea jumps 10 cn across the glass surface how far does its image jump across the screen? explain your reasoning.

Answer 1

4 cm/0.2 cm is the ratio 20:1

That is, the flea’s shadow will be 20 times its actual size. If it jumps 10 cm on the lens, then its image will be 20 times that distance or 200 cm on the screen.

Note: 0.2 cm = 2 millimeters

Answer 2

thanks, but why how is this the answer?

Answer 3

\(\bf \cfrac{4cm}{0.2cm}\qquad \qquad 0.2 = \cfrac{2}{10}\qquad thus\\ \quad \\
\cfrac{4cm}{0.2cm}\implies \cfrac{4cm}{\frac{2}{10}cm}\\ \quad \\
\textit{recall that}\qquad \cfrac{\quad \frac{a}{b}\quad }{\frac{c}{d}} = \cfrac{a}{b}\times\cfrac{d}{c}\\ \quad \\
\cfrac{4cm}{\frac{2}{10}cm}\implies \cfrac{4}{1}\times \cfrac{10}{2}\implies\cfrac{\cancel{40}}{\cancel{2}}\implies \cfrac{20}{1}\)

Answer 4

Very nice LaTeX.

Answer 5

hhehe.... I sorta cheat, using an editor =)