Question

Which of the following shows why parallelogram PQRS is congruent to parallelogram P'Q'R'S'?

A.
The parallelogram was rotated 180° clockwise about the origin and shifted 5 units in the y-direction.
B.
The parallelogram was rotated 90° clockwise about the origin and shifted -5 units in the y-direction.
C.
The parallelogram was rotated 90° clockwise about the origin and shifted 5 units in the x-direction.
D.
The parallelogram was rotated 180° clockwise about the origin and shifted -5 units in the x-direction.

Answer 1

The correct option is A because it describes a rotation of 180° and a shift of 5 units in the y-direction, which don't affect the congruency of the parallelogram.

Step-by-step explanation:

To determine why parallelogram PQRS is congruent to parallelogram P'Q'R'S', we need to analyze the transformations that were applied to parallelogram PQRS to obtain parallelogram P'Q'R'S'. Let's examine the given options and their effects on the initial parallelogram:

• A. The parallelogram was rotated 180° clockwise about the origin and shifted 5 units in the y-direction.
• B. The parallelogram was rotated 90° clockwise about the origin and shifted -5 units in the y-direction.
• C. The parallelogram was rotated 90° clockwise about the origin and shifted 5 units in the x-direction.
• D. The parallelogram was rotated 180° clockwise about the origin and shifted -5 units in the x-direction.

After considering the effects of each transformation, we can determine that option A is the correct choice. It describes a rotation of 180° (which doesn't change the shape) and a shift of 5 units in the y-direction, which doesn't alter the congruency of the parallelogram.

Answer 2

B

Step-by-step explanation:

1. First transformation is the rotation 90° clockwise about the origin. This transformation has the rule

(x,y)→(y,-x).

Then

• P(-6,6)→P''(6,6);
• Q(-2,6)→Q''(6,2);
• R(-3,2)→R''(2,3);
• S(-7,2)→S''(2,7).

2. The second transformation is translation 5 units down with the rule

(x,y)→(x,y-5).

Then

• P''(6,6)→P'(6,1);
• Q''(6,2)→Q'(6,-3);
• R''(2,3)→R'(2,-2);
• S''(2,7)→S'(2,2).