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.

9.55 degrees.

step-by-step explanation:

the given angle is

1 cycle is equal to 2π radians. so 4π will be equal to two cycles.

5.166667π-4π = 1.166667π

hence, this angle goes a little more than negative x axis.

1.166667π-π= 0.166667π

hence, the reference angle is 0.166667π radians.

1 radian = 57.2958 degrees

now, in degrees, this should be equals to 9.55 degrees.