Triangle tuv was dilated to create triangle t'u'v' using point a as the center of dilation. what is the scale factor of the dilation?

A dilation is a transformation, with center O and a scale factor of k that is not zero, that maps O to itself and any other point P to P'. The center O is a fixed point, P' is the image of P, points O, P and P' are on the same line.

Thus, a dilation with centre O and a scale factor of k maps the original figure to the image in such a way that the distances from O to the vertices of the image are k times the distances from O to the original figure. Also the size of the image are k times the size of the original figure.

In the dilation of triangle TUV, It is obvious that the image T'U'V' is smaller than the original triangle TUV and hence the scale factor is less than 1.

The ratio of the distances from A to the vertices of the image T'U'V'  to the distances from A to the original triangle TUV is the scale factor.

The scale factor = 3.2 / 4.8 = 2/3

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