# Geometry question: translating a rectangle according to a specific rule

Please take a look at the figure below. I have two line segments: a, which goes from point A to point B, and b, which goes from point B to point C. Each line defines a rectangle, which has width d and the line goes through the middle of it (along the longer edges of the rectangle). I want to find point D, given that I know the positions of point A, point B and point C and that D is at such a position, that the lower right edge of the new rectangle it forms (the green one) coincides with the right-most corner of the rectangle defined by line a. In other words, this transformation involves rotating the line a certain degree to the left with respect to point C and then shortening it so that point B coincides with point D (or the other way around - shortening it first and then rotating it).

So the first thing I did was to calculate the position of the right-most edge of the rectangle defined by line a thinking I could somehow get the slope of the green rectangle's shorter edge and get to D, knowing that the distance between the rightmost corner to D is d/2. However, I don;t know how to get that slope; this method is probably not the correct one. Do you have any ideas how to solve that?

Thank you in advance!

Edit: Does anyone see a way to solve that? Maybe there is not enough information to solve it?

• Are you translating the rectangle around line b to make the right corners coincide? From the figure it seems like you are doing some rotation too... – Aryabhata Jan 12 '15 at 6:03
• Yes, this is what I am doing. Yes, this transformation involves rotating the line and then shortening it, or the other way around. But I am not sure how to do that. – Hello Jan 12 '15 at 6:15
• Why don't you describe what you are doing, in the question statement? – Aryabhata Jan 12 '15 at 6:17
• I added a short description under the image. – Hello Jan 12 '15 at 6:22