Answer:
The scale factor of a dilation from ABCD to RSTU is [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
We know that the rectangle ABCD is similar to rectangle RSTU.
Given that in rectangle ABCD the longest sides are DC and AB and in the rectangle RSTU the longest sides are UT and RS ⇒ The scale factor of a dilation will transform the sides DC and AB into UT and RS
Working with the lengths of the sides :
DC.(Scale factor) = UT
AB.(Scale factor) = RS
Replacing with the values of the lengths (Scale factor : SF) :
[tex]DC.SF=UT\\(90ft).(SF)=45ft\\SF=\frac{45ft}{90ft} \\SF=\frac{1}{2}[/tex]
[tex]AB.SF=RS\\(90ft).(SF)=45ft\\SF=\frac{45ft}{90ft} \\SF=\frac{1}{2}[/tex]
Notice that the scale factor is dimensionless.
We can verify this result with the sides AD and BC :
[tex]AD.SF=UR\\50ft.(\frac{1}{2})=25ft\\ 25ft=25ft[/tex]
[tex]BC.SF=TS\\50ft.(\frac{1}{2})=25ft\\ 25ft=25ft[/tex]
The scale factor (SF) is [tex]\frac{1}{2}[/tex]
