Slicing piece 35 units wide off one side of triangle: need formula

JonnyRW

New member
Joined
Jan 16, 2018
Messages
3
Hi, this is my first post so I hope I've got the format ok.

This is a puzzle I seem to have landed myself in. It has a real-world application. I am tying myself in knots with trying to solve it:

I am to be given 3 coordinates which describe a triangle. (x1,y1)(x2,y2)(x3,y3) All sides will be at least 100 units long. I will be asked to remove a parallel "slice" 35 units wide off one of the sides. eg (x2,y2)(x3,y3). I'm trying to define a formula which will return the three new coordinates for any triangle and for any side being sliced.

Here's an example image. What formula would you suggest to find the new values (x1,y1) and (x2,y2), in red?

TriangleProblem.jpg
 
(x2,y2) is not in red. I would find the new (x1,y1) in the following way.

Similarly, one can find the new (x3,y3).

Step1, find the line equation of (x1,y1),(x3,y3), denote it as l1
Step2, find the line equation through (x2,y2) and perpendicular to l1, denote it as l2
Step3, find the intersection point p(x4,y4) of l1 and l2.
Step4, find the point (x5,y5) on l2 such that x4<x5 and the distance between (x4,y4) and (x5,y5) is 35.
Step5, find the line equation that pass (x5,y5) and parallel to l1, denoted it as l3
Step6, find the line equation of (x1,y1) and (x2,y2), denote it as l4
Step7, the intersection of l4 and l3 will give you the new red (x1,y1)
 
Thank you for your solution @yma16. How would you write this as a formula please?

Will this work for a deduction from any side?
 
How would you write this as a formula please?
Are you able to show any of your efforts, toward deriving a general formula?

Having the algorithm provided by yma16 in hand, can you start with that? Maybe you could begin again, by trying to streamline parts of the algorithm (i.e., using substitution, et cetera, to combine steps, expressing quantities in terms of others).


Will this [algorithm] work for a deduction from any side?
Have you tried using it, yet? What do you think? :cool:
 
Top