To find the scale factor of a dilation, we need to compare the corresponding sides of the original triangle ABC and the dilated triangle A'B'C'. The scale factor (k) is the ratio of the length of a side in the dilated triangle to the length of the corresponding side in the original triangle.
The formula to calculate the scale factor is:
For example, if side AB in triangle ABC is dilated to become A'B' in triangle A'B'C', we would calculate the scale factor as:
You would repeat this process for each pair of corresponding sides in the two triangles to determine the scale factor of the dilation.
By comparing the lengths of the corresponding sides of the two triangles, you can determine the scale factor of the dilation with point O as the center.
