Figure pqrs is rotated by 180 degrees about the origin in the counterclockwise direction to obtain figure p′q′r′s′:
which statement best compares the lengths of the sides of the two figures?

length of pq = length of p′q′
length of pq = length of r′s′
length of rs = length of p′q′
length of rs = length of q′r′

A. Length of PQ = Length of P′Q′

Step-by-step explanation:

We are given,

Figure PQRS is rotated by 180° counter-clockwise about the origin to obtain P'Q'R'S'.

Since, we know that, 'Rotation' is a transformation that turns the figure around a fixed point to a certain degree.

We get that, rotation does not affect the length of the figure.

So, the length of PQ = length of P'Q' and length of RS = length of R'S'

Thus, according to the options, we get that option A i.e. Length of PQ = Length of P′Q′ is correct.