Which of the following are the correct coordinates when the point (1,8) is rotated 180° anticlockwise about the origin?

To solve the problem of finding the coordinates of the point (1, 8) when rotated 180° anticlockwise about the origin, follow these steps:

1. Break Down the Problem

We need to perform a rotation transformation of the point (1, 8) by 180° around the origin.

2. Relevant Concepts

The formula for rotating a point $(x, y)$ 180° anticlockwise around the origin is: $(x', y') = (-x, -y)$ where $(x', y')$ are the new coordinates after rotation.

3. Analysis and Detail

Using the above formula with the coordinates of the point $(1, 8)$:

• Let $x = 1$ and $y = 8$.
• Applying the rotation formula: $x' = -1 \\ y' = -8$ Thus, the coordinates after rotation are: $(x', y') = (-1, -8)$

4. Verify and Summarize

After applying the transformation, we check:

• The original point (1, 8) has indeed been rotated 180° to result in the point (-1, -8).

Final Answer

The coordinates after rotating the point (1, 8) 180° anticlockwise about the origin are (-1, -8).