Question

give me the points of a shape on a graph after a 180-degree rotation counterclockwise
original points (-2, 2) (-2, 4) (-4, 2) (-4, 4) (-5, 3)

Answer 1

To perform a 180-degree rotation counterclockwise about the origin, you can use the following transformation rule for each point \((x, y)\):

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

Let's apply this transformation to each of the given points:

1. \((-2, 2)\):
\[
(-2, 2) \rightarrow (2, -2)
\]

2. \((-2, 4)\):
\[
(-2, 4) \rightarrow (2, -4)
\]

3. \((-4, 2)\):
\[
(-4, 2) \rightarrow (4, -2)
\]

4. \((-4, 4)\):
\[
(-4, 4) \rightarrow (4, -4)
\]

5. \((-5, 3)\):
\[
(-5, 3) \rightarrow (5, -3)
\]

So, the points after a 180-degree rotation counterclockwise are:

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

These are the new coordinates of the shape after the rotation.