Answer:
[tex]Scale\ Factor = 0.4[/tex]
Step-by-step explanation:
See attachment for complete question.
From the attachment, the following are the given parameters.
In PQRS
[tex]PQ = 20[/tex]
[tex]QR = 20[/tex]
[tex]RS = 15[/tex]
[tex]SP = 10[/tex]
In P'Q'R'S
[tex]P'Q' = 8[/tex]
[tex]Q'R' = 8[/tex]
[tex]R'S' = 6[/tex]
[tex]S'P' = 4[/tex]
Required
Determine the scale factor
The following is the relationship between a shape and its dilated image
[tex]Image = Original * Scale\ Factor[/tex]
In this case:
[tex]P'Q'R'S = PQRS * Scale\ Factor[/tex]
Make Scale Factor the subject:
[tex]Scale\ Factor = \frac{P'Q'R'S'}{PQRS}[/tex]
Take PQ and P'Q' as points of reference
[tex]Scale\ Factor = \frac{P'Q'}{PQ}[/tex]
Substitute values for PQ and P'Q'
[tex]Scale\ Factor = \frac{8}{20}[/tex]
[tex]Scale\ Factor = 0.4[/tex]
