Question

Square PQRS is rotated 90° clockwise using the origin as the center of rotation.

On a coordinate plane, square P Q R S has points (negative 2, 2), (negative 2, negative 1), (1, negative 1), (1, 2).

Which graph shows the image P’Q’R’S’?
On a coordinate plane, square P prime Q prime R prime S prime has points (2, 2), (negative 1, 2), (negative 1, negative 1), (2, negative 1).
On a coordinate plane, square P prime Q prime R prime S prime has points (negative 1, negative 1), (2, negative 1), (2, 2), (negative 1, 2).
On a coordinate plane, square P prime Q prime R prime S prime has points (negative 2, negative 2), (1, negative 2), (1, 1), (negative 2, 1).
On a coordinate plane, square P prime Q prime R prime S prime has points (1, 1), (negative 2, 1), (negative 2, negative 2), (1, negative 2).

Answer 1

To find the coordinates of the square PQRS after a 90° clockwise rotation around the origin, we can use the transformation rules for rotations. Rotating a point \((x, y)\) 90° clockwise results in the new point \((y, -x)\).

Let's apply this to each point of square PQRS with the points given:

1. **Point P (-2, 2)**
- New coordinates: \( (2, 2) \)

2. **Point Q (-2, -1)**
- New coordinates: \( (-1, 2) \)

3. **Point R (1, -1)**
- New coordinates: \( (-1, -1) \)

4. **Point S (1, 2)**
- New coordinates: \( (2, -1) \)

Thus, the new coordinates after the 90° clockwise rotation are:
- P' (2, 2)
- Q' (-1, 2)
- R' (-1, -1)
- S' (2, -1)

Now we can compare these coordinates to the given options:

1. **Option 1:** Points - (2, 2), (-1, 2), (-1, -1), (2, -1) - This option matches our calculated coordinates.

2. **Option 2:** Does not match.

3. **Option 3:** Does not match.

4. **Option 4:** Does not match.

Therefore, the correct option that shows the image P'Q'R'S' after the 90° clockwise rotation is:

**On a coordinate plane, square P' Q' R' S' has points (2, 2), (-1, 2), (-1, -1), (2, -1).**