To find the image vertices for a dilation centered at the origin (0, 0) with a scale factor of 4, you’ll follow a straightforward process.
A dilation transformation involves enlarging or reducing the size of a shape based on a given center point and scale factor. In this case, our center is the origin and the scale factor is 4, meaning we will enlarge the shape by a factor of 4.
- Identify the original vertices: Before performing the dilation, you need the coordinates of the initial vertices of the shape you are working with. For example, let’s say we have a triangle with vertices at points A(1, 2), B(3, 4), and C(5, 1).
- Apply the dilation formula: The formula to calculate the coordinates of the image vertices after dilation is:
(x', y') = (kx, ky), where(x, y)are the original coordinates,kis the scale factor, and(x', y')are the new coordinates after dilation. - Calculate new vertices: Now, apply the scale factor of 4 to each original vertex:
– For vertex A(1, 2):
(x', y') = (4 * 1, 4 * 2) = (4, 8)
– For vertex B(3, 4):
(x', y') = (4 * 3, 4 * 4) = (12, 16)
– For vertex C(5, 1):
(x', y') = (4 * 5, 4 * 1) = (20, 4)
Thus, the image vertices after dilation are:
- Image of A: (4, 8)
- Image of B: (12, 16)
- Image of C: (20, 4)
In summary, to find the image vertices for a dilation with center at the origin and a scale factor of 4, simply multiply each coordinate of the original vertices by 4. This method ensures the shape remains similar but becomes four times larger!