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:
-
\((-2, 2)\): \[ (-2, 2) \rightarrow (2, -2) \]
-
\((-2, 4)\): \[ (-2, 4) \rightarrow (2, -4) \]
-
\((-4, 2)\): \[ (-4, 2) \rightarrow (4, -2) \]
-
\((-4, 4)\): \[ (-4, 4) \rightarrow (4, -4) \]
-
\((-5, 3)\): \[ (-5, 3) \rightarrow (5, -3) \]
So, the points after a 180-degree rotation counterclockwise are:
- \((2, -2)\)
- \((2, -4)\)
- \((4, -2)\)
- \((4, -4)\)
- \((5, -3)\)
These are the new coordinates of the shape after the rotation.