Rotate the shape; (-2,1),(0,1),(0,4),(-1,4),(-2,3) to 180 degrees counterclockwise

Answer 1

To rotate a point \((x, y)\) by 180 degrees counterclockwise around the origin, you can use the formula:

\[ (x', y') = (-x, -y) \]

Now, let's apply this formula to each of the points you provided:

1. Point (-2, 1): \[ (-(-2), -1) = (2, -1) \]

2. Point (0, 1): \[ (-(0), -1) = (0, -1) \]

3. Point (0, 4): \[ (-(0), -4) = (0, -4) \]

4. Point (-1, 4): \[ (-(-1), -4) = (1, -4) \]

5. Point (-2, 3): \[ (-(-2), -3) = (2, -3) \]

So, the rotated points are:

1. \( (2, -1) \)
2. \( (0, -1) \)
3. \( (0, -4) \)
4. \( (1, -4) \)
5. \( (2, -3) \)

Thus, the rotated shape has the vertices:

• \( (2, -1) \)
• \( (0, -1) \)
• \( (0, -4) \)
• \( (1, -4) \)
• \( (2, -3) \)