Question

Imagine a counterclockwise rotation of 270° about the origin of the figure. Choose the coordinate of A′ . (1 point) Responses (2,−1) left parenthesis 2 comma negative 1 right parenthesis (−1,−2) left parenthesis negative 1 comma negative 2 right parenthesis (1,2) left parenthesis 1 comma 2 right parenthesis (1,1)

Answer 1

The original coordinate of A is, (-2,1)

Answer 2

To find the new coordinates of point A after a counterclockwise rotation of 270° about the origin, we can follow these steps:

1. **Understanding Rotation**: A counterclockwise rotation of 270° is equivalent to a clockwise rotation of 90°.

2. **Rotation Transformation**: The transformation rules for rotation are:
- A 90° clockwise rotation transforms the point \((x, y)\) to \((y, -x)\).

3. **Applying the Transformation**:
Let's apply the transformation to point A. Since the coordinates of A are not provided, I'll demonstrate the process generally.

If point A has coordinates \((x, y)\):
- After a 90° clockwise rotation, the new coordinates A' will be:
\[
A' = (y, -x)
\]

4. **Example**:
Let's say the original coordinates of A were \((1, 1)\). Using the transformation:
- \(x = 1\) and \(y = 1\) gives:
\[
A' = (1, -1)
\]

5. **Select from Given Options**:
Now, we compare our calculated point A' from the options provided:
1. (2, -1)
2. (-1, -2)
3. (1, 2)
4. (1, 1)

Since we don't have the specific coordinates for A, it's difficult to determine the exact answer unless we know the original coordinates.

However, according to the transformation we discussed, the final answer will depend on the original coordinates of point A. With this information missing, please provide the coordinates of point A for an exact calculation.

Answer 3

Given the original coordinates of point A as \((-2, 1)\), we will apply a counterclockwise rotation of 270° (which is equivalent to a clockwise rotation of 90°) about the origin.

### Rotation Rules
For a 90° clockwise rotation, the transformation from \((x, y)\) to \((y, -x)\) is used.

### Step-by-Step Transformation
1. **Original Coordinates**:
\[
A = (-2, 1)
\]

2. **Apply the Transformation**:
- Using the transformation rule \((x, y) \rightarrow (y, -x)\):
\[
A' = (1, -(-2)) = (1, 2)
\]

### Conclusion
After the counterclockwise rotation of 270° about the origin, the new coordinates of point A, denoted as A', are:
\[
\boxed{(1, 2)}
\]

This matches one of the options provided!