Question

Parallelogram ABCD is rotated to create image A'B'C'D'.

On a coordinate plane, 2 parallelograms are shown. The first parallelogram has points A (2, 5), B (5, 4), C (5, 2), D (2, 3). The second parallelogram has points A prime (5, negative 2), B prime (4, negative 5), C prime (2, negative 5), D prime (3, negative 2).
Which rule describes the transformation?

(x, y) → (y, –x)
(x, y) → (–y, x)
(x, y) → (–x, –y)
(x, y) → (x, –y

Answer 1

To determine the transformation rule that describes the rotation of parallelogram ABCD to its image A'B'C'D', we can compare the coordinates of the original points with the coordinates of the transformed points.

Original points:
- A (2, 5)
- B (5, 4)
- C (5, 2)
- D (2, 3)

Transformed points:
- A' (5, -2)
- B' (4, -5)
- C' (2, -5)
- D' (3, -2)

Now let's apply each transformation rule to point A (2, 5) and see which one matches the corresponding point A' (5, -2).

1. **Rule**: (x, y) → (y, –x)
- Applying to A: (2, 5) → (5, -2)
- This matches point A'.

2. **Rule**: (x, y) → (–y, x)
- Applying to A: (2, 5) → (-5, 2)
- This does not match point A'.

3. **Rule**: (x, y) → (–x, –y)
- Applying to A: (2, 5) → (-2, -5)
- This does not match point A'.

4. **Rule**: (x, y) → (x, –y)
- Applying to A: (2, 5) → (2, -5)
- This does not match point A'.

Thus, the transformation that maps ABCD to A'B'C'D' is:

**(x, y) → (y, –x)**.