Question

Your house is located at: A (-2,1); B( 0,1); C(0,3); D(-1,4); E(-2,3)
what are the new points if you rotate the house 180 degrees counterclockwise about the origin?

Answer 1

To rotate points 180 degrees counterclockwise about the origin, you can use the transformation rule that changes the coordinates (x, y) to (-x, -y).

Let's apply this transformation to each point of the house:

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

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

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

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

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

Now, let's summarize the new points after the 180-degree rotation about the origin:

- A' = (2, -1)
- B' = (0, -1)
- C' = (0, -3)
- D' = (1, -4)
- E' = (2, -3)

These are the coordinates of the house after the rotation.