find the image vertices for a dilation with center (0,0) and a scale factor of 4
To find the image vertices for a dilation, we need to apply the scale factor to each vertex.
Let's consider an example with a square. The vertices of the square are (x, y), where x and y are the coordinates.
Given a scale factor of 4 and a center of dilation at (0, 0), the coordinates of the original square's vertices are:
1. Vertex A: (x1, y1)
2. Vertex B: (x2, y2)
3. Vertex C: (x3, y3)
4. Vertex D: (x4, y4)
To find the image vertices, we need to apply the scale factor to each coordinate pair:
1. Vertex A':
x1' = 4 * x1
y1' = 4 * y1
2. Vertex B':
x2' = 4 * x2
y2' = 4 * y2
3. Vertex C':
x3' = 4 * x3
y3' = 4 * y3
4. Vertex D':
x4' = 4 * x4
y4' = 4 * y4
The image vertices after the dilation will be:
1. A': (x1', y1')
2. B': (x2', y2')
3. C': (x3', y3')
4. D': (x4', y4')
Now you just need to substitute the values of x1, y1, x2, y2, x3, y3, x4, and y4 into the equations above to calculate the coordinates of the image vertices.