To find the image of point e after applying a dilation centered at the origin (0,0) with a scale factor of 6, we first need to know the coordinates of point e. Let’s assume that point e has coordinates (x, y).
A dilation with a scale factor of k multiplies the coordinates of a point by k. In our case, k is 6, so the new coordinates (x’, y’) of the image of point e will be calculated as follows:
- x’ = 6 * x
- y’ = 6 * y
For example, if point e is at (1, 2), after performing the dilation:
- x’ = 6 * 1 = 6
- y’ = 6 * 2 = 12
So, the image of point e would be (6, 12). This dilation not only scales the distance from the origin but also maintains the direction of the point.
In conclusion, the coordinates of point e are multiplied by 6 to determine its image after dilation. This process can be applied to any point defined in a two-dimensional space.