Composition of Two Dilations

Author:
Jon Ingram
This shows the result of composing two dilations (enlargements): A, then B. Dilation A is represented in blue: you can change the centre and the scale factor. Dilation B is represented in red: you can change the centre and the scale factor. The check boxes alter what you see. You can see the result of dilation A (initially hidden), arrows which show what happen to the vertices of the quadrilateral (initially shown) and lines which demonstrate whether or not the composition really is a dilation (initially hidden). Is the composition of two dilations also a dilation? If so, where is the centre?
You can: * Investigate when happens when the quadrilateral is moved. * Decide whether or not the composite transformation is or isn't a dilation, and if so where the centre of the dilation is. * Investigate what happens when the centres of each individual dilation are moved. * Investigate when happens when the scale factors of each individual dilation are moved. This interactivity was inspired by a tweet by James Tanton.