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Given:
Scale factor
Center of dilation = (4,2)
To find:
The coordinates of the points C' and A.
Solution:
We know that, if a figure is dilated with a scale factor k and the center of dilation is at the point (a,b), then
The scale factor is and the center of dilation is at (4,2).
...(i)
Suppose the vertices of red triangle are A(m,n), B(10,14) and C(-2,11).
Using rule (i), we get
Hence, the coordinates of Point C' are C'(2,5).
Let us assume that point A is A(m,n).
Using rule (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).