Dilation of a Point
To perform a dilation on a point with a scale factor centered at the origin, you simply multiply the x and y coordinates of the point by the scale factor. For the point (6, 12) and a scale factor of \( \frac{1}{2} \), the calculation would be as follows:
- The x-coordinate after dilation: \( 6 \times \frac{1}{2} = 3 \)
- The y-coordinate after dilation: \( 12 \times \frac{1}{2} = 6 \)
Therefore, the image of the point (6, 12) after a dilation with a scale factor of \( \frac{1}{2} \) centered at the origin is (3, 6).
