The point W(–2,6) is rotated 180° counterclockwise around the origin. What are the coordinates of the resulting point, W'?

1. Break Down the Problem

To find the coordinates of point W after a 180° counterclockwise rotation around the origin, we need to understand how the rotation affects the coordinates.

2. Relevant Concepts

When a point $(x, y)$ is rotated 180° around the origin, the new coordinates $(x', y')$ can be calculated using the following transformation: $(x', y') = (-x, -y)$

3. Analysis and Detail

Given the point W: $W(-2, 6)$ we apply the transformation:

• The x-coordinate becomes $-(-2) = 2$
• The y-coordinate becomes $-6$

Thus, the new coordinates are: $W' = (2, -6)$

4. Verify and Summarize

To verify, we double-check the transformation. The original x and y were $-2$ and $6$, respectively. After applying the transformation for a 180° rotation:

• New x: $2$
• New y: $-6$

Both calculations are consistent with the rotation rules.

Final Answer

The coordinates of the resulting point $W'$ after a 180° counterclockwise rotation around the origin are: $W'(2, -6)$