To find the image vertices after a dilation, we need to apply the dilation transformation to each of the original vertices. A dilation with a center at (0,0) and a scale factor of 4 means that each vertex will be moved away from the origin by a factor of 4.
The formula for dilating a point (x, y) with respect to the origin (0,0) is:
(x', y') = (kx, ky)
where k is the scale factor and (x’, y’) are the coordinates of the dilated point.
In our case, the scale factor k is 4. Therefore, if we have original vertices such as:
- (x1, y1)
- (x2, y2)
- (x3, y3)
We can calculate the dilated vertices as:
- (4x1, 4y1)
- (4x2, 4y2)
- (4x3, 4y3)
To summarize, after performing the dilation on each vertex by multiplying both the x and y coordinates by 4, you will get the new coordinates for the image vertices. This process essentially stretches the shape while keeping its proportions the same, centered at the origin.