Question

Two similar polygons are shown below:

Which transformation was performed on PQRS to form P′Q′R′S′?


A dilation factor of 2
A dilation factor of 4
A dilation factor of 1 over 2
A dilation factor of 1 over 4

Answer 1

a dilation of 2 was performed (:

Answer 2

Answer:  The correct option is (A) A dilation factor of 2.

Step-by-step explanation:  We are shown two similar polygons in the figure.

We are to select the transformation that was performed on PQRS to form P'Q'R'S'.

We can see clearly from the figure that two polygons have same shape but different sizes.

So, the only transformation possible from PQRS to P'Q'R'S' is dilation.

To find the dilation factor, we need the lengths of any two corresponding sides of PQRS and P'Q'R'S'.

From the graph, we note that

PQ = 2 units  and P'Q' = 4 units.

Therefore, the dilation factor is given by

$D_f\\\\\\=\dfrac{\textup{length of a side of the dilated figure P'Q'R'S'}}{\textup{length of the corresponding side of the original figure PQRS}}\\\\\\=\dfrac{P'Q'}{PQ}\\\\\\=\dfrac{4}{2}\\\\=2.$

Thus, the required transformation is a dilation with dilation factor of 2.

Option (A) is CORRECT.