Making a rectangle out of a line segment

Question

I have a line shown below in black. I want to make the line into a rectangle with added distance d.

The black line is the original line.I'm trying to calculate points A, B, C, and D. In order to calculate the new starting and end points of the line I figure out the slope and then use the formula below to calculate the the new start and end points of the line.

How would I then proceed to get the points A, B, C and D?

Answer 1

Great question!

Once you have your new start and end points for your new line, the next step is to use those points, along with the slope of the line, to get to your A,B,C,D points.

For this to be a rectangle, you new lines (AB and CD) must be perpendicular to your original line. So, once you've found the slope of the black line, the slope of the blue lines must be the opposite reciprocal of the slope of your black line.

For example: If the slope of the black line is 3/5, the slope of your blue lines should be -5/3. Once you have that, you can use the same process as before (using your formula) to find your A,B,C, and D points.

Hope this points you in the right direction!