Answer:
a) k = 5; (-10, -35)
Step-by-step explanation:
Given:
Co-ordinates:
Pre-Image = (-12,3)
After dilation
Image = (-60,15)
The dilation about the origin can be given as :
Pre-Image
where  represents the scalar factor.
 represents the scalar factor.
We can find value of  for the given co-ordinates by finding the ratio of
 for the given co-ordinates by finding the ratio of  or
 or  co-ordinates of the image and pre-image.
 co-ordinates of the image and pre-image.

For the given co-ordinates. 
Pre-Image = (-12,3)
Image = (-60,15)
The value of 
or 
As we get  for both ratios i.e of
 for both ratios i.e of  and
 and   co-ordinates, so we can say the image has been dilated by a factor of 5 about the origin.
 co-ordinates, so we can say the image has been dilated by a factor of 5 about the origin.
To find the image of (-2,-7), after same dilation, we will multiply the co-ordinates with the scalar factor.
Pre-Image Image
 Image
Pre-Image Image
 Image (Answer)
 (Answer)