Question

A square gets rotated 180 counterclockwise, what's the location now? The corners of the square are A, B, C, D

A: -10, 6
B: -7, 6
C: -7, 3
D: -10, 3

Answer 1

To rotate a point 180 degrees counterclockwise around the origin, you can use the transformation:

\[
(x, y) \rightarrow (-x, -y)
\]

Let's apply this transformation to the corners of the square:

1. **Point A (-10, 6)**:
\[
A': (-(-10), -6) = (10, -6)
\]

2. **Point B (-7, 6)**:
\[
B': (-(-7), -6) = (7, -6)
\]

3. **Point C (-7, 3)**:
\[
C': (-(-7), -3) = (7, -3)
\]

4. **Point D (-10, 3)**:
\[
D': (-(-10), -3) = (10, -3)
\]

So after rotating the square 180 degrees counterclockwise, the new coordinates for the corners are:

- \( A' : (10, -6) \)
- \( B' : (7, -6) \)
- \( C' : (7, -3) \)
- \( D' : (10, -3) \)

If we summarize the new positions:

- A' = (10, -6)
- B' = (7, -6)
- C' = (7, -3)
- D' = (10, -3)

Thus, the locations of the corners after the rotation are:

- A': (10, -6)
- B': (7, -6)
- C': (7, -3)
- D': (10, -3)