Question

Rectangle ABCD is similar to rectangle RSTU .

What is the scale factor of a dilation from ABCD to RSTU ?

Enter your answer in the box.

Answer 1

0.5

Explanation:

The correct answer they will be looking for is 0.5

Answer 2

The scale factor of a dilation from ABCD to RSTU is
`(1)/(2)`

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) :

`DC.SF=UT\\(90ft).(SF)=45ft\\SF=(45ft)/(90ft) \\SF=(1)/(2)`

`AB.SF=RS\\(90ft).(SF)=45ft\\SF=(45ft)/(90ft) \\SF=(1)/(2)`

Notice that the scale factor is dimensionless.

We can verify this result with the sides AD and BC :

`AD.SF=UR\\50ft.((1)/(2))=25ft\\ 25ft=25ft`

`BC.SF=TS\\50ft.((1)/(2))=25ft\\ 25ft=25ft`

The scale factor (SF) is
`(1)/(2)`