Question

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

Answer 1

II only

Explanation:

A rotation is a transformation in which the figure rotates around a fixed point. In this case, the point of rotation is the origin.

Rotate the square 180° about the origin.

The resulting image has all the same angles and side measures as the original figure. Since side QR is parallel to side PS and side QP is parallel to side RS, side Q'R' is parallel to side P'S' and side Q'P' is parallel to side R'S'.

Therefore, the set of sides in II only would be parallel in the resulting image.

Answer 2

A. II only is correct.

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.