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A dilation 
is a dilation with a scale factor, k centered at the origin.
A scale factor, k means that the distance of the image from the the center of dilation is k times the distance of the pre-image from the center of dilation and the size of the image is k times the size of the pre-image.
Given triangle ABC with vertices A(-2, 2), B(1, 2) and C(1, -1), a dilation will result in the image with vertices A'2.5(-2, 2) = A'(-5, 5), B'2.5(1, 2) = B'(2.5, 5) and C'2.5(1, -1) = C'(2.5, -2.5)
Now, consider line AC, the equation of the line is given by
Notice that line y = -x is a line passing through the origin which is the center of dilation.
Consider line A'C', the equation of the line is given by
As an be seen the line AC and the line A'C' is the same line.
A scale factor, k means that the distance of the image from the the center of dilation is k times the distance of the pre-image from the center of dilation and the size of the image is k times the size of the pre-image.
Given triangle ABC with vertices A(-2, 2), B(1, 2) and C(1, -1), a dilation
Now, consider line AC, the equation of the line is given by
Notice that line y = -x is a line passing through the origin which is the center of dilation.
Consider line A'C', the equation of the line is given by
As an be seen the line AC and the line A'C' is the same line.