Question

Two similar polygons are shown below:

Which set of transformations was performed on PQRS to form P′Q′R′S′?

A dilation factor of 2
A dilation factor of 1 over 3
A dilation factor of 1 over 2
A dilation factor of 3

Answer 1

the correct answer would be a dialation of 1 over 3 as P'Q'R'S' is smaller than PQRS and its a third of its size.

Answer 2

Answer:  The correct set of transformations is (B) A dilation factor of 1 over 3.

Step-by-step explanation:  We are given to similar polygons PQRS and P'Q'R'S'.

We are to select the correct set of transformations that was performed on the polygon PQRS to form P'Q'R'S'.

Since the two polygons PQRS and P'Q'R'S' are similar, so there will be a dilation with a dilation (scale) factor.

We need to find the dilation factor of the dilation.

In P'Q'R'S', the length of a side is given by

P'Q' = 2 units,

and the length of the corresponding side in PQRS is given by

PQ = 2 units.

Therefore, the dilation factor of dilation is

$D=\dfrac{\textup{length of a side of }P'Q'R'S'}{\textup{length of the corresponding side in }PQRS}\\\\\\\Rightarrow S=\dfrac{P'Q'}{PQ}=\dfrac{2}{6}=\dfrac{1}{3}.$

Thus, there will be a dilation with a dilation factor of $\dfrac{1}{3}.$

Option (B) is correct.