Given:
The scale factor is  and the center of dilation is at the point (4,2).
 and the center of dilation is at the point (4,2).
Red is original figure and green is dilated figure.
To find:
The coordinates of point C' and point A.
Solution:
Rule of dilation: If a figure is dilated with a scale factor k and the center of dilation is at the point (a,b), then
 
According to the given information, the scale factor is  and the center of dilation is at (4,2).
 and the center of dilation is at (4,2).
 ...(i)
            ...(i)
Let us assume the vertices of red triangle are A(m,n), B(10,14) and C(-2,11).
Using (i), we get
 
 
 
 
Therefore, the coordinates of Point C' are C'(2,5).
We assumed that point A is A(m,n).
Using (i), we get
 
From the given figure it is clear that the image of point A is (8,4).
 
On comparing both sides, we get
 
 
 
 
 
And,
 
 
 
 
 
Therefore, the coordinates of point A are (16,8).