Question

Given a dilation with the origin O (0, 0), by observation determine the scale factor "K." DO, K = (5, 0) (10, 0) The dilation an expansion.

Answer 1

A dilation is a transformation $D_{o,\, k}$, 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.

In a dilation of $D_{o,\, k}$ the scale factor, k is mapping 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.

Thus for a  dilation using the rule $D_{o,\ k}=(5,\, 0)\rightarrow (10,\, 0)$ results in the distance of the image form O being twice the distance of the original point from O.

Therefore, it can be observed that the scale factor of the dilation, k, is 2.