Question

On a coordinate plane, B C D E has points (3, negative 1), (3, 1), (4, 1), (4, negative 1). R S P Q has points (negative 1, 4), (1, 4), (1, 3), (negative 1, 3). L M J K has points (negative 4, negative 1), (negative 4, 1), (negative 3, 1), (negative 3, negative 1).
Which statements are correct based on the graph? Select all that apply.
BCDE is rotated 90° to form JKLM.
PQRS is rotated 90° to form JKLM.
BCDE is rotated 180° to form JKLM.
JKLM is rotated 180° to form BCDE.
PQRS is rotated 180° to form BCDE.

Answer 1

To determine which statements are correct based on the relationships between the geometric figures represented by the given sets of points (BCDE, PQRS, and JKLM), let's first classify the coordinates and positions of each shape.

- BCDE consists of the points:
- B(3, -1)
- C(3, 1)
- D(4, 1)
- E(4, -1)

This is a vertical rectangle with the vertical sides parallel to the y-axis and horizontal sides parallel to the x-axis, extending from (3, -1) to (4, 1).

- PQRS consists of the points:
- P(-1, 4)
- Q(1, 4)
- R(1, 3)
- S(-1, 3)

This is a horizontal rectangle with the horizontal sides at y = 3 and y = 4, and extending from (-1, 3) to (1, 4).

- JKLM consists of the points:
- J(-4, -1)
- K(-4, 1)
- L(-3, 1)
- M(-3, -1)

This is also a vertical rectangle similar in orientation to BCDE, extending from (-4, -1) to (-3, 1).

### Now, let's analyze the statements:

1. **BCDE is rotated 90° to form JKLM.**
- This is **incorrect**. A 90° rotation would move BCDE to a different orientation, not matching the position of JKLM.

2. **PQRS is rotated 90° to form JKLM.**
- This is **incorrect**. A 90° rotation would not map the points correctly as the dimensions and alignments differ.

3. **BCDE is rotated 180° to form JKLM.**
- This is **correct**. A 180° rotation around the origin would yield the corresponding points of JKLM.

4. **JKLM is rotated 180° to form BCDE.**
- This is **correct**. A 180° rotation of JKLM around the origin results in the formation of BCDE.

5. **PQRS is rotated 180° to form BCDE.**
- This is **incorrect**. PQRS would not map to BCDE with a 180° rotation as the shapes and dimensions do not align.

### Summary of correct statements:
- BCDE is rotated 180° to form JKLM.
- JKLM is rotated 180° to form BCDE.

Thus, the correct statements based on the graph are:
- BCDE is rotated 180° to form JKLM.
- JKLM is rotated 180° to form BCDE.