What happens to the coordinates of a point under a dilation with a scale factor of 2?

In a dilation transformation, every point in the plane is moved away from or towards a fixed point (the center of dilation) based on a specific scale factor. When the scale factor is 2, this means that each coordinate of a point will be multiplied by 2.

For example, if you have a point with coordinates (x, y), under dilation with a scale factor of 2, the new coordinates would be (2x, 2y). This multiplication effectively enlarges the size of the figure represented by the point while maintaining the same shape, as distances from the center of dilation to any points on the figure are doubled.

In contrast, subtracting, dividing, or adding to the coordinates would change their values in ways that do not correspond to a simple scaling transformation. Therefore, multiplying the coordinates by the scale factor accurately reflects the nature of dilation.