Construction image under homothety with compass and ruler. Find the image of line segment AB under the homothety with center O and ratio k = 2. Draw rays from point O through points A, B. With compass find point A' that line segment OA' is two times longer as OA. In the same way find point B'. Join points A' and B'. We get the image of the line segment AB under the homothety with center O and ratio k = 2.