Let's find the images of three points under three different scale transformations: D2, D1/2, and D10.
The image of a point under a scale transformation Dk(x) is calculated by multiplying the point's coordinates by the scale factor k.
1. When applying D2 to the point (1, -5), we multiply the coordinates of point 1 (which are 1 and -5) by the scale factor 2:
- For the x-coordinate: 1 * 2 = 2
- For the y-coordinate: -5 * 2 = -10
So, the image of this point under D2 is (2, -10).
2. When applying D1/2 to the point (0.6), there is only the x-coordinate available so:
- For the x-coordinate: 0.6 * 1/2 = 0.3
So, the image of this point under D1/2 is (0.3).
3. When applying D10 to the point (0, 0), we multiply the scale factor 10 with the point's coordinates (which are 0 and 0):
- For the x-coordinate: 0 * 10 = 0
- For the y-coordinate: 0 * 10 = 0
So, the image of the origin point (0, 0) is still (0, 0), no matter what the scale factor is.
In conclusion, the images of the points (1,-5), (0.6), and (0,0) under the transformations D2, D1/2, and D10 are, respectively, (2,-10), (0.3), and (0,0).