Question

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