Question

a flea is 0.2 cm long. as it walks across the glass surface of an overhead projector, its image on the screen appears to be 4cm long. what is the scale factor of the dilation? if the flea jumps 10cm across the glass surface, how far does its image jump across the screen?

Answer 1

if you are 3 feet tall and your shadow is 9 feet tall, by what factor is your shadow larger than you?

Answer 2

3?

Answer 3

yes, so your shadow is 4 times as big as you. so the scale factor between you and your shadow is 1:3

Answer 4

1:3 means " one is to three". so if one is to three, then 10 is to ?

Answer 5

so for the first part of the problem it would be 1:2 and the second it would be 2:1?

Answer 6

no no. If you are 0.2 feet tall and your shadow is 4 feet tall, what is the scale factor?

Answer 7

4/.2 = 20?

Answer 8

yes. so the scale factor between the projected image and the actual flea size is 20:1

Answer 9

note that if you say the scale factor of the flea size to the projected image, it would be 1:20

Answer 10

so be careful. the scale factor is a relative term. It depends on whether you are comparing the magnified object to the actual object or the other way round.

Answer 11

what about if the flea jumps 10cm across the glass surface, how far does its image jump across the screen?

Answer 12

okay so we have established that the scale factor to the projected image is 20 times the actual size.

Answer 13

20x10?

Answer 14

so if the flea actually jumps 10 cm, yes, it jumps 20X10 = 200 cm on the screen.

Answer 15

good job.

Answer 16

how would you explain your reasoning?

Answer 17

I just did in detail.

Answer 18

thankyou hb what is the distance between a point and its image after the translation (x,y) --> (x+7, y-5) ?

Answer 19

http://www.purplemath.com/modules/distform.htm