If square pqrs is rotated 180° about the origin to create square p'q'r's', which set of sides would be parallel in the resulting image?

i. p'q' and q'r'
ii. q'r' and p's'
iii. p'q' and s'p'
iv. q'r' and r's'

a.
ii only
b.
iii only
c.
i and iv only
d.
i and ii only

A. II only is correct.

Step-by-step explanation:

We are given the square PQRS with co-ordinates P(2,-5), Q(4,-3), R(6,-5) and S(4,-7).

As, we know that,

Reflection about 180° changes the co-ordinates (x,y) to (-x,-y).

So, the co-ordinates of P'Q'R'S' are given by,

P'(-2,-5), Q'(-4,-3), R'(-6,-5) and S'(-4,-7).

So, from the figure below, we see that,

P'Q' is parallel to S'R'

Q'R' is parallel to P'S'.

So, according to the options, we have,

Option II i.e. Q'R' is parallel to P'S' is correct.

Thus, option A is correct.